
Paolo BORDONE
Professore Associato Dipartimento di Scienze Fisiche, Informatiche e Matematiche sede exFisica

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2024
 Characterization of partially accessible anisotropic spin chains in the presence of antisymmetric exchange
[Articolo su rivista]
Cavazzoni, Simone; Adani, Marco; Bordone, Paolo; Paris, Matteo G. A.
abstract
We address quantum characterization of anisotropic spin chains in the presence of antisymmetric exchange, and investigate whether the Hamiltonian parameters of the chain may be estimated with precision approaching the ultimate limit imposed by quantum mechanics. At variance with previous approaches, we focus on the information that may be extracted by measuring only two neighboring spins rather than a global observable on the entire chain. We evaluate the Fisher information (FI) of a twospin magnetization measure, and the corresponding quantum Fisher
information (QFI), for all the relevant parameters, i.e. the spin coupling, the anisotropy, and the Dzyaloshinskii–Moriya (DM) parameter. Our results show that the reduced system made of two neighboring spins may be indeed exploited as a probe to characterize global properties of the entire system. In particular, we find that the ratio between the FI and the QFI is close to unit for a large range of the coupling values. The DM coupling is beneficial for coupling estimation, since it leads
to the presence of additional bumps and peaks in the FI and QFI, which are not present in a model that neglects exchange interaction and may be exploited to increase the robustness of the overall estimation procedure. Finally, we address the multiparameter estimation problem, and show that the model is compatible but sloppy, i.e. both the Uhlmann curvature and the determinant of the QFI matrix vanish. Physically, this means that the state of the system actually depends only on a
reduced numbers of combinations of parameters, and not on all of them separately.
2024
 Coin dimensionality as a resource in quantum metrology involving discretetime quantum walks
[Articolo su rivista]
Cavazzoni, Simone; Razzoli, Luca; Ragazzi, Giovanni; Bordone, Paolo; Paris, Matteo G. A.
abstract
We address metrological problems where the parameter of interest is encoded in the internal degree of freedom of a discretetime quantum walker, and provide evidence that coin dimensionality is a potential resource to enhance precision. In particular, we consider estimation problems where the coin parameter governs rotations
around a given axis and show that the corresponding quantum Fisher information (QFI) may increase with the dimension of the coin. We determine the optimal initial state of the walker to maximize the QFI and discuss whether, and to what extent, precision enhancement may be achieved by measuring only the position of the
walker. Finally, we consider Groverlike encoding of the parameter and compare results with those obtained from rotation encoding.
2023
 Quantum estimation and remote charge sensing with a holespin qubit in silicon
[Articolo su rivista]
Forghieri, Gaia; Secchi, Andrea; Bertoni, Andrea; Bordone, Paolo; Troiani, Filippo
abstract
Holespin qubits in semiconductors represent a mature platform for quantum technological applications.
Here we consider their use as quantum sensors, and specifically for inferring the presence and estimating the distance from the qubit of a remote charge. Different approaches are considered, based on the use of single or double quantum dots, ground and outofequilibrium states, Rabi and Ramsey measurements, and comparatively analyzed by means of the discrimination probability, and of the classical and quantum Fisher information.
Detailed quantitative aspects result from the multiband character of the hole states, which we account for by means of the LuttingerKohn Hamiltonian. Furthermore, general conclusions can be drawn on the relative
efficiency of the above options, and analytical expressions are derived for the Fisher information of a generic qubit within the Rabi and Ramsey schemes.
2022
 Perturbed graphs achieve unit transport efficiency without environmental noise
[Articolo su rivista]
Cavazzoni, S.; Razzoli, L.; Bordone, P.; Paris, M. G. A.
abstract
Coherent transport of an excitation through a network corresponds to continuoustime quantum walk on a graph, and the transport properties of the system may be radically different depending on the graph and on the initial state. The transport efficiency, i.e., the integrated probability of trapping at a certain vertex, is a measure of the success rate of the transfer process. Purely coherent quantum transport is known to be less efficient than the observed excitation transport, e.g., in biological systems, and there is evidence that environmental noise is indeed crucial for excitation transport. At variance with this picture, we here address purely coherent transport on highly symmetric graphs, and show analytically that it is possible to enhance the transport efficiency without environmental noise, i.e., using only a minimal perturbation of the graph. In particular, we show that adding an extra weight to one or two edges, depending on whether the initial state is localized or in a superposition of two vertex states, breaks the inherent symmetries of the graph and may be sufficient to achieve unit transport efficiency. We also briefly discuss the conditions to obtain a null transport efficiency, i.e., to avoid trapping.
2022
 Timedependent transport in graphene MachZender interferometers
[Articolo su rivista]
Forghieri, Gaia; Bordone, Paolo; Bertoni, Andre
abstract
Graphene nanoribbons provide an ideal platform for electronic interferometry in the integer quantum Hall regime. Here, we solve the timedependent fourcomponent Schrödinger equation for single carriers in graphene and expose several dynamical effects of the carrier localization on their transport characteristics in pn junctions.
We simulate two kinds of MachZender interferometers (MZI). The first is based on quantum point contacts and is similar to traditional GaAs/AlGaAs interferometers. As expected, we observe AharonovBohm oscillations and phase averaging. The second is based on valley beam splitters, where we observe unexpected phenomena
due to the intersection of the edge channels that constitute the MZI. Our results provide further insights into the behavior of graphene interferometers. Additionally, they highlight the operative regime of such nanodevices for
feasible singleparticle implementations.
2022
 Universality of the fully connected vertex in Laplacian continuoustime quantum walk problems
[Articolo su rivista]
Razzoli, Luca; Bordone, Paolo; A Paris, Matteo G
abstract
A fully connected vertex w in a simple graph G of order N is a vertex connected
to all the other N − 1 vertices. Upon denoting by L the Laplacian matrix
of the graph, we prove that the continuoustime quantum walk (CTQW)—with
Hamiltonian H = γL—of a walker initially localized at w does not depend
on the graph G. We also prove that for any Groverlike CTQW—with Hamiltonian
H = γL +
w λww w—the probability amplitude at the fully connected
marked vertices w does not depend on G. The result does not hold for
CTQW with Hamiltonian H = γA (adjacency matrix). We apply our results to
spatial search and quantum transport for single and multiple fully connected
marked vertices, proving that CTQWs on any graph G inherit the properties
already known for the complete graph of the same order, including the optimality
of the spatial search. Our results provide a unified framework for several
partial results already reported in literature for fully connected vertices, such as
the equivalence of CTQWand of spatial search for the central vertex of the star
and wheel graph, and any vertex of the complete graph.
2021
 Pauli principle and the Monte Carlo method for charge transport in graphene
[Articolo su rivista]
Coco, Marco; Bordone, Paolo; Demeio, Lucio; Romano, Vittorio
abstract
An attempt to include the Pauli principle in the Monte Carlo method by also acting on the freeflight step and
not only at the end of each collision is investigated. The charge transport in suspended monolayer graphene is
considered as a test case. The results are compared with those obtained with the standard ensemble Monte Carlo
technique and with the updated direct simulation Monte Carlo algorithm which is able to correctly handle with
Pauli’s principle. The physical aspects of the investigated approach are analyzed as well.
2021
 Role of topology in determining the precision of a finite thermometer
[Articolo su rivista]
Candeloro, Alessandro; Razzoli, Luca; Bordone, Paolo; Paris, Matteo G. A.
abstract
Temperature fluctuations of a finite system follow the Landau bound δT 2 = T 2/C(T ) where C(T ) is the heat
capacity of the system. In turn, the same bound sets a limit to the precision of temperature estimation when
the system itself is used as a thermometer. In this paper, we employ graph theory and the concept of Fisher
information to assess the role of topology on the thermometric performance of a given system. We find that low
connectivity is a resource to build precise thermometers working at low temperatures, whereas highly connected
systems are suitable for higher temperatures. Upon modeling the thermometer as a set of vertices for the quantum
walk of an excitation, we compare the precision achievable by position measurement to the optimal one, which
itself corresponds to energy measurement.
2021
 Transport Efficiency of ContinuousTime Quantum Walks on Graphs
[Articolo su rivista]
Razzoli, Luca; Paris, Matteo G. A.; Bordone, Paolo
abstract
Continuoustime quantum walk describes the propagation of a quantum particle (or an
excitation) evolving continuously in time on a graph. As such, it provides a natural framework
for modeling transport processes, e.g., in lightharvesting systems. In particular, the transport
properties strongly depend on the initial state and specific features of the graph under investigation.
In this paper, we address the role of graph topology, and investigate the transport properties of
graphs with different regularity, symmetry, and connectivity. We neglect disorder and decoherence,
and assume a single trap vertex that is accountable for the loss processes. In particular, for each
graph, we analytically determine the subspace of states having maximum transport efficiency. Our
results provide a set of benchmarks for environmentassisted quantum transport, and suggest
that connectivity is a poor indicator for transport efficiency. Indeed, we observe some specific
correlations between transport efficiency and connectivity for certain graphs, but, in general, they
are uncorrelated.
2021
 Wigner function with correlation damping
[Articolo su rivista]
Barletti, Luigi; Bordone, Paolo; Demeio, Lucio; Giovannini, Elisa
abstract
We examine the effect of the decoherenceinduced reduction of correlation length on a onedimensional
scattering problem by solving numerically the evolution equation for the Wigner function with decoherence
proposed by Barletti et al. [J. Comput. Theor. Transp. 47, 209 (2018)]. The numerical solution is achieved by
the splittingscheme algorithm, suitably modified to include the decoherence term. Three cases are examined,
corresponding to a reflectiondominated regime, a transmissiondominated regime, and an intermediate one.
The dynamic evolution of the Wigner function is followed until the separation process of the reflected and
of the transmitted packets is complete and it is observed for three different values of the correlation length.
The outcomes show a broadening and flattening of the Wigner function which becomes progressively more
pronounced as the correlation length is decreased. This results in a reduced reflection at low energies and in a
reduced transmission at high energies.
2020
 Continuoustime quantum walks in the presence of a quadratic perturbation
[Articolo su rivista]
Candeloro, Alessandro; Razzoli, Luca; Bordone, Paolo; Paris, Matteo G. A.
abstract
We address the properties of continuoustime quantum walks with Hamiltonians of the form H = L + λL2,
with L the Laplacian matrix of the underlying graph and the perturbation λL2 motivated by its potential use to
introduce nextnearestneighbor hopping. We consider cycle, complete, and star graphs as paradigmatic models
with low and high connectivity and/or symmetry. First, we investigate the dynamics of an initially localized
walker. Then we devote attention to estimating the perturbation parameter λ using only a snapshot of the
walker dynamics. Our analysis shows that a walker on a cycle graph spreads ballistically independently of the
perturbation, whereas on complete and star graphs one observes perturbationdependent revivals and strong
localization phenomena. Concerning the estimation of the perturbation, we determine the walker preparations
and the simple graphs that maximize the quantum Fisher information. We also assess the performance of
position measurement, which turns out to be optimal, or nearly optimal, in several situations of interest. Besides
fundamental interest, our study may find applications in designing enhanced algorithms on graphs.
2020
 Continuoustime quantum walks on planar lattices and the role of the magnetic field
[Articolo su rivista]
Razzoli, Luca; Paris, Matteo; Bordone, Paolo
abstract
We address the dynamics of continuoustime quantum walk (CTQW) on planar twodimensional (2D) lattice
graphs, i.e., those forming a regular tessellation of the Euclidean plane (triangular, square, and honeycomb lattice graphs). We first consider the free particle: On square and triangular lattice graphs we observe the wellknown ballistic behavior, whereas on the honeycomb lattice graph we obtain a subballistic one, although still faster than the classical diffusive one. We impute this difference to the different amount of coherence generated by the evolution and, in turn, to the fact that, in 2D, the square and the triangular lattices are Bravais lattices, whereas the honeycomb one is nonBravais. From the physical point of view, this means that CTQWs are not universally characterized by the ballistic spreading. We then address the dynamics in the presence of a perpendicular uniform magnetic field and study the effects of the field by two approaches: (i) introducing the Peierls phase factors, according to which the tunneling matrix element of the free particle becomes complex or (ii) spatially discretizing the Hamiltonian of a spinless charged particle in the presence of a magnetic field. Either way, the dynamics of an initially localized walker is characterized by a lower spread compared to the free particle case; larger
fields correlate to more localized stays of the walker. Remarkably, upon analyzing the dynamics by spatial
discretization of the Hamiltonian (vector potential in the symmetric gauge), we obtain that the variance of the
space coordinate is characterized by pseudooscillations, a reminiscence of the harmonic oscillator behind theHamiltonian in the continuum, whose energy levels are the wellknown Landau levels.
2020
 Twoelectron selective coupling in an edgestate based conditional phase shifter
[Articolo su rivista]
Bellentani, Laura; Forghieri, Gaia; Bordone, Paolo; Bertoni, Andrea
abstract
We investigate the effect of longrange Coulomb interaction on the twoelectron scattering in the integer
quantum Hall regime at bulk filling factor two.We compute the dynamics of the exact twoparticle wave function
by means of a parallel version of the splitstep Fourier method in a 2D potential background reproducing the
effect of depleting gates in a realistic heterostructure, with the charge carrier represented by a localized wave
packet of edge states.We compare the spatial shift induced by Coulomb repulsion in the final twoelectron wave
function for two indistinguishable electrons initialized in different configurations according to their Landau index
and analyze their bunching probability and the effect of screening. We finally prove the feasibility of this device
as a twoqubit conditional phase shifter able to generate controlled entanglement from product states.
2019
 A Proposal for Evading the Measurement Uncertainty in Classical and Quantum Computing: Application to a Resonant Tunneling Diode and a
MachZehnder Interferometer
[Articolo su rivista]
Pandey, Devashish; Bellentani, Laura; Villani, Matteo; Albareda, Guillermo; Bordone, Paolo; Bertoni, Andrea; Oriols, Xavier
abstract
Measuring properties of quantum systems is governed by a stochastic (collapse
or statereduction) law that unavoidably yields an uncertainty (variance) associated with the
corresponding mean values. This nonclassical source of uncertainty is known to be manifested
as noise in the electrical current of nanoscale electron devices, and hence it can flaw the good
performance of more complex quantum gates. We propose a protocol to alleviate this quantum
uncertainty that consists of (i) redesigning the device to accommodate a large number of electrons
inside the active region, either by enlarging the lateral or longitudinal areas of the device and
(ii) renormalizing the total current to the number of electrons. How the above two steps can be
accommodated using the present semiconductor technology has been discussed and numerically
studied for a resonant tunneling diode and a MachZehnder interferometer, for classical and quantum
computations, respectively. It is shown that the resulting protocol formally resembles the socalled
collective measurements, although, its practical implementation is substantially different.
2019
 Coulomb and exchange interaction effects on the exact twoelectron dynamics
in the HongOuMandel interferometer based on Hall edge states
[Articolo su rivista]
Bellentani, Laura; Bordone, Paolo; Oriols, Xavier; Bertoni, Andrea
abstract
The electronic HongOuMandel interferometer in the integer quantum Hall regime is an ideal system to probe
the building up of quantum correlations between charge carriers and it has been proposed as a viable platform for
quantum computing gates. Using a parallel implementation of the splitstep Fourier method, we simulated the
antibunching of two interacting fermionic wave packets impinging on a quantum point contact. Numerical results
of the exact approach are compared with a simplified theoretical model based on onedimensional scattering
formalism. We show that, for strongly localized wave packets in a fullscale geometry, the Coulomb repulsion
dominates over the exchange energy, this effect being strongly dependent on the energy broadening of the
particles. We define analytically the spatial entanglement between the two regions of the quantum point contact,
and obtain quantitatively its entanglementgeneration capabilities.
2019
 Lattice quantum magnetometry
[Articolo su rivista]
Razzoli, Luca; Ghirardi, Luca; Siloi, Ilaria; Bordone, Paolo; Paris, Matteo G. A.
abstract
We put forward the idea of lattice quantum magnetometry, i.e., quantum sensing of magnetic fields by a
charged (spinless) particle placed on a finite twodimensional lattice. In particular, we focus on the detection
of a locally static transverse magnetic field, either homogeneous or inhomogeneous, by performing groundstate
measurements. The system turns out to be of interest as a quantum magnetometer, since it provides
nonnegligible quantum Fisher information (QFI) in a large range of configurations. Moreover, the QFI shows
some relevant peaks, determined by the spectral properties of the Hamiltonian, suggesting that certain values of
the magnetic fields may be estimated better than others, depending on the value of other tunable parameters. We
also assess the performance of coarsegrained position measurement, showing that it may be employed to realize
nearly optimal estimation strategies.
2019
 Quantum computing with quantumHall edge state interferometry
[Articolo su rivista]
Bordone, Paolo; Bellentani, Laura; Bertoni, Andrea
abstract
Electron interferometers based on Hall edge states (ESs) proved to be robust demonstrators of
the coherent quantum dynamics of carriers. Several proposals to expose their capability to build
and control quantum entanglement and to exploit them as building block for quantum computing
devices has been presented. Here, we review the timedependent numerical modeling of Hall
interferometers operating at the singlecarrier level at integer filling factor (FF). By defining the
qubit state either as the spatial localization (at FF 1) or the Landau index (at FF 2) of a single
carrier propagating in the ES, we show how a generic onequbit rotation can be realized. By a
proper design of the twodimensional electron gas potential landscape, an entangling twoqubit
gate can be implemented by exploiting Coulomb interaction, thus realizing a universal set of
quantum gates. We also assess how the shape of the edge confining potential affects the visibility
of the quantum transformations.
2018
 Back and forth from Fock space to Hilbert space: a guide for commuters
[Articolo su rivista]
Beggi, Andrea; Siloi, Ilaria; Benedetti, Claudia; Piccinini, Enrico; Razzoli, Luca; Bordone, Paolo; Paris, Matteo G. A.
abstract
Quantum states of systems made of many identical particles, e.g. those
described by Fermi–Hubbard and Bose–Hubbard models, are conveniently
depicted in the Fock space. However, in order to evaluate some specific
observables or to study system dynamics, it is often more effective to employ
the Hilbert space description. Moving effectively from one description to the
other is thus a desirable feature, especially when a numerical approach is
needed. Here we recall the construction of the Fock space for systems of
indistinguishable particles, and then present a set of recipes and advice for
students and researchers with the need to commute back and forth from one
description to the other. The twoparticle case is discussed in some detail, and
a few guidelines for numerical implementations are given.
2018
 Dynamics and Halledgestate mixing of localized electrons in a twochannel
MachZehnder interferometer
[Articolo su rivista]
Bellentani, Laura; Beggi, Andrea; Bordone, Paolo; Bertoni, Andrea
abstract
We present a numerical study of a multichannel electronicMachZehnder interferometer, based onmagnetically
driven noninteracting edge states. The electron path is defined by a fullscale potential landscape on the twodimensional
electron gas at filling factor 2, assuming initially only the first Landau level as filled.We tailor the two
beamsplitters with 50% interchannelmixing and measure AharonovBohm oscillations in the transmission probability
of the second channel.We perform timedependent simulations by solving the electron Schrödinger equation
through a parallel implementation of the splitstep Fourier method, and we describe the chargecarrier wave function
as a Gaussian wave packet of edge states.We finally develop a simplified theoretical model to explain the features
observed in the transmission probability, and we propose possible strategies to optimize gate performances.
2018
 Probing the sign of the Hubbard interaction by twoparticle quantum walks
[Articolo su rivista]
Beggi, Andrea; Razzoli, Luca; Bordone, Paolo; Paris, Matteo G. A.
abstract
We address the discrimination between attractive and repulsive interaction in systems made of two identical bosons propagating on a onedimensional lattice, and suggest a probing scheme exploiting the dynamical properties of the corresponding twoparticle quantum walks. In particular, we show that the sign of the interaction leaves a clear signature in the dynamics of the two walkers, which is governed by the Hubbard model, and in their quantum correlations, thus permitting one to discriminate between the two cases. We also prove that these features are strictly connected to the band structure of the Hubbard Hamiltonian.
2018
 Quantum metrology at level anticrossing
[Articolo su rivista]
Ghirardi, Luca; Siloi, Ilaria; Bordone, Paolo; Troiani, Filippo; Paris, Matteo G. A.
abstract
We address parameter estimation in twolevel systems exhibiting level anticrossing and prove that universally optimal strategies for parameter estimation may be designed. In fact, we find a parameterindependent measurement scheme, leading to the ultimate quantum precision, independently of the value of the parameter of interest. Optimal estimationmay be achieved also at high temperature, depending on the structure of the twolevel Hamiltonian. Finally, we discuss parameter estimation based on dynamical strategies, and a number of specific applications.
2017
 Dynamics of copropagating edge states in a multichannel MachZender interferometer
[Relazione in Atti di Convegno]
Bellentani, L.; Beggi, A.; Bordone, P.; Bertoni, A.
abstract
We study numerically a multichannel electronic MachZender interferometer, where
an orthogonal magnetic field produces edge states. Our timedependent model is based on the splitstep Fourier method and describes the charge carrier as a Gaussian wavepacket of edge states, whose path is defined by splitgate induced potential profiles on the 2DEG at filling factor 2. We analyse a beam splitter with ∼ 50% interchannel mixing and obtain AharonovBohm oscillations in the transmission probability of the second channel.
2017
 GPUaccelerated algorithms for manyparticle continuoustime quantum walks
[Articolo su rivista]
Piccinini, Enrico; Benedetti, Claudia; Siloi, Ilaria; Paris, Matteo G. A.; Bordone, Paolo
abstract
Manyparticle continuoustime quantum walks (CTQWs) represent a resource for several tasks in quantum technology, including quantum search algorithms and universal quantum computation. In order to design and implement CTQWs in a realistic scenario, one needs effective simulation tools for Hamiltonians that take into account static noise and fluctuations in the lattice, i.e. Hamiltonians containing stochastic terms. To this aim, we suggest a parallel algorithm based on the Taylor series expansion of the evolution operator, and compare its performances with those of algorithms based on the exact diagonalization of the Hamiltonian or a 4th order Runge–Kutta integration. We prove that both Taylorseries expansion and Runge–Kutta algorithms are reliable and have a low computational cost, the Taylorseries expansion showing the additional advantage of a memory allocation not depending on the precision of calculation. Both algorithms are also highly parallelizable within the SIMT paradigm, and are thus suitable for GPGPU computing. In turn, we have benchmarked 4 NVIDIA GPUs and 3 quadcore Intel CPUs for a 2particle system over lattices of increasing dimension, showing that the speedup provided by GPU computing, with respect to the OPENMP parallelization, lies in the range between 8x and (more than) 20x, depending on the frequency of postprocessing. GPUaccelerated codes thus allow one to overcome concerns about the execution time, and make it possible simulations with many interacting particles on large lattices, with the only limit of the memory available on the device. Program summary Program Title: cuQuWa Licensing provisions: GNU General Public License, version 3 Program Files doi: http://dx.doi.org/10.17632/vjpnjgycdj.1 Programming language: CUDA C Nature of problem: Evolution of manyparticle continuoustime quantumwalks on a multidimensional grid in a noisy environment. The submitted code is specialized for the simulation of 2particle quantumwalks with periodic boundary conditions. Solution method: Taylorseries expansion of the evolution operator. The densitymatrix is calculated by averaging multiple independent realizations of the system. External routines: cuBLAS, cuRAND Unusual features: Simulations are run exclusively on the graphic processing unit within the CUDA environment. An undocumented misbehavior in the randomnumber generation routine (cuRAND package) can corrupt the simulation of large systems, though no problems are reported for small and mediumsize systems. Compiling the code with the arch=sm_30 flag for compute capability 3.5 and above fixes this issue.
2017
 Noisy quantum walks of two indistinguishable interacting particles
[Articolo su rivista]
Siloi, Ilaria; Benedetti, Claudia; Piccinini, Enrico; Piilo, Jyrki; Maniscalco, Sabrina; Paris, Matteo G. A.; Bordone, Paolo
abstract
We investigate the dynamics of continuoustime twoparticle quantum walks on a onedimensional noisy lattice. Depending on the initial condition, we show how the interplay between particle indistinguishability and interaction determines distinct propagation regimes. A realistic model for the environment is considered by introducing nonGaussian noise as timedependent fluctuations of the tunneling amplitudes between adjacent sites. We observe that the combined effect of particle interaction and fast noise (weak coupling with the environment) provides a faster propagation compared to the noiseless case. This effect can be understood in terms of the band structure of the Hubbard model, and a detailed analysis as a function of both noise and system parameters is presented.
2017
 Quantum walks of two interacting particles on percolation graphs
[Relazione in Atti di Convegno]
Siloi, Ilaria; Benedetti, Claudia; Piccinini, Enrico; Paris, Matteo G. A.; Bordone, Paolo
abstract
We address the dynamics of two indistinguishable interacting particles moving on
a dynamical percolation graph, i.e., a graph where the edges are independent random telegraph
processes whose values jump between 0 and 1, thus mimicking percolation. The interplay
between the particle interaction strength, initial state and the percolation rate determine
different dynamical regimes for the walkers. We show that, whenever the walkers are initially
localised within the interaction range, fast noise enhances the particle spread compared to the
noiseless case.
2016
 NonMarkovian continuostime quantum walks on lattices with dynamical noise
[Articolo su rivista]
Claudia, Benedetti; Buscemi, Fabrizio; Bordone, Paolo; Matteo G. A., Paris
abstract
We address the dynamics of continuoustime quantum walks on onedimensional disordered lattices inducing dynamical noise in the system. Noise is described as timedependent fluctuations of the tunneling amplitudes between adjacent sites, and attention is focused on nonGaussian telegraph noise, going beyond the usual assumption of fast Gaussian noise. We observe the emergence of two different dynamical behaviors for the walker, corresponding to two opposite noise regimes: slow noise (i.e., strong coupling with the environment) confines the walker into few lattice nodes, while fast noise (weak coupling) induces a transition between quantum and classical diffusion over the lattice. A phase transition between the two dynamical regimes may be observed by tuning the ratio between the autocorrelation time of the noise and the coupling between the walker and the external environment generating the noise. We also address the nonMarkovianity of the quantum map by assessing its memory effects, as well as evaluating the information backflow to the system. Our results suggest that the nonMarkovian character of the evolution is linked to the dynamical behavior in the slow noise regime, and that fast noise induces a Markovian dynamics for the walker.
2016
 Quantum correlations of identical particles subject to classical environmental noise
[Articolo su rivista]
Beggi, Andrea; Buscemi, Fabrizio; Bordone, Paolo
abstract
Abstract In this work, we propose a measure for the quantum discord of indistinguishable
particles, based on the definition of entanglement of particles given in
Wiseman and Vaccaro (Phys Rev Lett 91:097902, 2003. doi:10.1103/PhysRevLett.91.
097902). This discord of particles is then used to evaluate the quantum correlations in
a system of two identical bosons (fermions), where the particles perform a quantum
random walk described by the Hubbard Hamiltonian in a 1D lattice. The dynamics of
the particles is either unperturbed or subject to a classical environmental noise—such
as random telegraph, pink or brown noise. The observed results are consistent with
those for the entanglement of particles, and we observe that onsite interaction between
particles have an important protective effect on correlations against the decoherence
of the system.
2016
 Transient and Oscillating response of Ovonic devices for highspeed electronics
[Articolo su rivista]
Piccinini, Enrico; Brunetti, Rossella; Bordone, Paolo; Rudan, Massimo; Jacoboni, Carlo
abstract
The electric response of Ovonic devices to a timedependent voltage is analysed by means of a chargetransport model previously proposed by the authors. The numerical implementation of the model shows that the features of the I(V) characteristics depend not only upon the external bias, but also on more complex effects due to the interplay between intrinsic microscopic relaxation times and the inevitable parasitic elements of the system.
Either stable or oscillating solutions are found according to the position of the load line. The model also allows for speculations on the potential of Ovonic materials in the design of selector devices for twoterminal nonvolatile memories.
2015
 Analytical expression of genuine tripartite quantum discord for symmetrical Xstates
[Articolo su rivista]
Beggi, Andrea; Buscemi, Fabrizio; Bordone, Paolo
abstract
The study of classical and quantum correlations in bipartite and multipartite
systems is crucial for the development of quantum information theory. Among
the quantifiers adopted in tripartite systems, the genuine tripartite quantum discord
(GTQD), estimating the amount of quantum correlations shared among all the subsystems,
plays a key role since it represents the natural extension of quantum discord used
in bipartite systems. In this paper, we derive an analytical expression of GTQD for
threequbit systems characterized by a subclass of symmetrical Xstates. Our approach
has been tested on both GHZ and maximally mixed states reproducing the expected
results. Furthermore, we believe that the procedure here developed constitutes a valid
guideline to investigate quantum correlations in form of discord in more general multipartite
systems.
2015
 Timedependent modelling of singleelectron interferometry with edgestates
[Relazione in Atti di Convegno]
Beggi, Andrea; Bertoni, Andrea; Bordone, Paolo
abstract
We simulate the timeresolved dynamics of localized electrons in a 2DEG system,
where an external magnetic eld creates quantum Hall edge states, and properly polarized split
gates dene a MachZehnder electron interferometer. The carriers travelling inside the Hall
channels consist of localized wave packets of edge states: they are propagated numerically by
means of a Fourier splitstep approach. We find that the energydependent scattering process at
the quantum point contacts, together with the nite energy distribution of the carriers, have a
remarkable eect on the transmission coecient T of the device. We provide an analytical model
to justify the characteristics of T which is in good agreement with the numerical simulations.
2015
 Timedependent simulation and analytical modelling of electronic MachZehnder interferometry with edgestates wave packets
[Articolo su rivista]
Beggi, Andrea; Bordone, Paolo; Buscemi, Fabrizio; Bertoni, Andrea
abstract
We compute the exact singleparticle timeresolved dynamics of electronic Mach–Zehnder
interferometers based on Landau edgestates transport, and assess the effect of the spatial
localization of carriers on the interference pattern. The exact carrier dynamics is obtained by
solving numerically the timedependent Schrödinger equation with a suitable 2D potential
profile reproducing the interferometer design. An external magnetic field, driving the system
to the quantum Hall regime with filling factor one, is included. The injected carriers are
represented by a superposition of edge states, and their interference pattern—controlled
via magnetic field and/or area variation—reproduces the one of (Ji et al 2003 Nature 422
415). By tuning the system towards different regimes, we find two additional features in the
transmission spectra, both related to carrier localization, namely a damping of the Aharonov–
Bohm oscillations with increasing difference in the arms length, and an increased mean
transmission that we trace to the energydependent transmittance of quantum point contacts.
Finally, we present an analytical model, also accounting for the finite spatial dispersion of the
carriers, able to reproduce the above effects.
2014
 Quantum probes for the spectral properties of a classical environment
[Articolo su rivista]
Claudia, Benedetti; Buscemi, Fabrizio; Bordone, Paolo; Matteo G. A., Paris
abstract
We address the use of simple quantum probes for the spectral characterization of classical noisy environments.
In our scheme a qubit interactswith a classical stochastic field describing environmental noise and is thenmeasured
after a given interaction time in order to estimate the characteristic parameters of the noise. In particular, we
address estimation of the spectral parameters of two relevant kinds of nonGaussian noise: random telegraph
noise with a Lorentzian spectrum and colored noise with a 1/f α spectrum. We analyze in detail the estimation
precision achievable by quantum probes and prove that population measurement on the qubit is optimal for
noise estimation in both cases. We also evaluate the optimal interaction times for the quantum probe, i.e., the
values maximizing the quantum Fisher information (QFI) and the quantum signaltonoise ratio. For random
telegraph noise the QFI is inversely proportional to the square of the switching rate, meaning that the quantum
signaltonoise ratio is constant and thus the switching rate may be uniformly estimated with the same precision
in its whole range of variation. For colored noise, the precision achievable in the estimation of “color,” i.e., of the
exponent α, strongly depends on the structure of the environment, i.e., on the number of fluctuators describing
the classical environment. For an environment modeled by a single random fluctuator estimation is more precise
for pink noise, i.e., for α = 1, whereas by increasing the number of fluctuators, the quantum signaltonoise ratio
has two local maxima, with the largest one drifting towards α = 2, i.e., brown noise.
2014
 Wigner transport equation with finite coherence length
[Articolo su rivista]
Carlo, Jacoboni; Bordone, Paolo
abstract
The use of the Wigner function for the study of
quantum transport in open systems is subject to severe criticisms.
Some of the problems arise from the assumption of
infinite coherence length of the electron dynamics outside
the system of interest. In the present work the theory of
the Wigner function is revised assuming a finite coherence
length. A new dynamical equation is found, corresponding
to move the Wigner momentum off the real axis, and a numerical
analysis is performed for the case of study of the
onedimensional potential barrier. In quantum device simulations,
for a sufficiently long coherence length, the new formulation
does not modify the physics in any finite region of
interest but it prevents mathematical divergence problems.
2013
 Dynamics of quantum correlations in colorednoise environments
[Articolo su rivista]
C., Benedetti; F., Buscemi; Bordone, Paolo; M. G. A., Paris
abstract
We address the dynamics of entanglement and quantum discord for two noninteracting qubits initially prepared
in a maximally entangled state and then subjected to a classical colored noise, i.e., coupled with an external
environment characterized by a noise spectrum of the form 1/f α.More specifically, we address systems in which
the Gaussian approximation fails, i.e., mere knowledge of the spectrum is not enough to determine the dynamics
of quantum correlations. We thus investigate the dynamics for two different configurations of the environment:
in the first case, the noise spectrum is due to the interaction of each qubit with a single bistable fluctuator with
an undetermined switching rate, whereas in the second case we consider a collection of classical fluctuators with
fixed switching rates. In both cases, we found analytical expressions for the time dependence of entanglement
and quantum discord, which may also be extended to a collection of fluctuators with random switching rates.
The environmental noise is introduced by means of stochastic timedependent terms in the Hamiltonian, and this
allows us to describe the effects of both separate and common environments. We show that the nonGaussian
character of the noise may lead to significant effects, e.g., environments with the same power spectrum, but
different configurations give rise to the opposite behavior for quantum correlations. In particular, depending
on the characteristics of the environmental noise considered, both entanglement and discord display either a
monotonic decay or the phenomena of sudden death and revivals. Our results show that the microscopic structure
of the environment, in addition to its noise spectrum, is relevant for the dynamics of quantum correlations and
may be a valid starting point for the engineering of nonGaussian colored environments.
2013
 Time evolution of tripartite quantum discord and entanglement under local and nonlocal random telegraph noise
[Articolo su rivista]
F., Buscemi; Bordone, Paolo
abstract
Few studies explored the dynamics of nonclassical correlations besides entanglement in open multipartite
quantum systems. Here, we address the time evolution of quantum discord and entanglement in a model of
three noninteracting qubits subject to a classical random telegraph noise in common and separated environments.
Two initial entangled states of the system are examined, namely the GHZ and Wtype states. The dynamics
of quantum correlations results to be strongly affected by the input configuration of the qubits, the type of the
systemenvironment interaction, and the memory properties of the environmental noise. When the qubits are
nonlocally coupled to the random telegraph noise, the GHZtype states partially preserve, at long times, both
discord and entanglement, regardless of the correlation time of the environmental noise. The survived entangled
states turn out to be also detectable by means of suitable entanglement witnesses. On the other hand, in the same
conditions, the decohering effects suppress all the quantum correlation of the Wtype states which are thus less
robust than the GHZtype ones. The longtime survival of tripartite discord and entanglement opens interesting
perspectives in the use of multipartite entangled states for practical applications in quantum information science.
2013
 Timeevolution of entanglement and quantum discord of bipartite systems subject to 1/f^a noise
[Relazione in Atti di Convegno]
Claudia, Benedetti; Matteo G. A., Paris; Fabrizio, Buscemi; Bordone, Paolo
abstract
We study the dynamics of quantum correlations for two non interacting qubits initially prepared in a maximally entangled state and then coupled with an external environment characterized by a noise spectrum of the form 1/f^α. The noise spectrum is due to the interaction of each qubit with a collection of Nf classical fluctuators with fixed switching rates. We find that, depending on the characteristic of the noise spectrum considered, both entanglement and quantum discord display either a monotonic decay or the phenomena of sudden death and revivals.
2012
 EFFECT OF MARKOV AND NONMARKOV CLASSICAL NOISE ON ENTANGLEMENT DYNAMICS
[Articolo su rivista]
Bordone, Paolo; F., Buscemi; C., Benedetti
abstract
We analyze the effect of a classical noise into the entanglement dynamics between two particles, initially entangled, subject to continuous time quantum walks in a onedimensional lattice. The noise is modeled by randomizing the transition amplitudes from one site to another. Both Markovian and nonMarkovian environments are considered. For the Markov regime an exponential decay of the initial quantum correlation is found, while the loss of coherence of the quantum state increases monotonically with time up to a saturation value depending upon the degrees of freedom of the system. For the nonMarkov regime the presence or absence of entanglement revival and entanglement sudden death phenomena is found or deduced depending on the peculiar characteristics of the noise. Our results indicate that the entanglement dynamics in the nonMarkovian regime is affected by the persistence of the memory effects of the environment and by its intrinsic features.
2012
 EFFECTS OF CLASSICAL ENVIRONMENTAL NOISE ON ENTANGLEMENT AND QUANTUM DISCORD DYNAMICS
[Articolo su rivista]
C., Benedetti; F., Buscemi; Bordone, Paolo; M. G. A., Paris
abstract
We address the effect of classical noise on the dynamics of quantum correlations, entanglement and quantum discord (QD), of two noninteracting qubits initially prepared in a Bell state. The effect of noise is modeled by randomizing the singlequbit transition amplitudes. We address both static and dynamic environmental noise corresponding to interaction with separate and common baths in either Markovian and nonMarkovian regimes. In the Markov regime, a monotone decay of the quantum correlations is found, whereas for nonMarkovian noise sudden death and revival phenomena may occur, depending on the characteristics of the noise. Entanglement and QD show the same qualitative behavior for all kind of noises considered. On the other hand, we find that separate and common environments may play opposite roles in preserving
quantum correlations, depending on the noise regime considered.
2012
 Electron interference and entanglement in coupled 1D systems with noise
[Articolo su rivista]
F., Buscemi; Bordone, Paolo; A., Bertoni
abstract
We estimate the role of noise in the formation of entanglement and in the appearance of single and twoelectron interference in systems of coupled onedimensional channels. Two cases are considered: a singleparticle interferometer and a twoparticle interferometer exploiting Coulomb interaction. In both
of them, environmental noise yields a randomization of the carrier phases. Our results assess how the
complementarity relation linking singleparticle behavior to nonlocal quantities (such as entanglement
and environmentinduced decoherence) acts in electron interferometry. We show that in an experimental
implementation of the setups examined, one and twoelectron detection probability at the output drains
can be used to evaluate the decoherence and the degree of entanglement.
2012
 Quantum correlations in continuoustime quantum walks of two indistinguishable particles
[Articolo su rivista]
C., Benedetti; F., Buscemi; Bordone, Paolo
abstract
We evaluate the degree of quantum correlation between two fermions (bosons) subject to continuous time quantum walks in a onedimensional ring lattice with periodic boundary conditions. In our approach, no particleparticle interaction is considered. We show that the interference effects due to exchangesymmetry can result into the appearance of nonclassical correlations. The role played onto the appearance of quantum correlations by the quantum statistics of the particles, the boundary conditions, and the partition of the systemis widely investigated. Quantum correlations have also been investigated in a model mimicking the ballistic evolution of two indistinguishable particles in a 1D continuous space structure.Our results are consistent with recent quantum optics and electron quantum optics experiments where the showing up of twoparticle nonclassical correlations has been observed even in the absence of mutual interaction between the particles.
2011
 Entanglement creation in semiconductor quantum dot charge qubit
[Articolo su rivista]
F., Buscemi; Bordone, Paolo; A., Bertoni
abstract
We study theoretically the appearance of quantum correlations in two and threeelectron scattering in single and double dots. The key role played by transport resonances into entanglement formation between the singleparticle states is shown. Both reflected and transmitted components of the scattered particle wavefunction are used to evaluate the quantum correlations between the incident carrier and the bound particle(s) in the dots. Our investigation provides a guideline for the analysis of decoherence effects due to the Coulomb scattering in semiconductor quantum dots structures.
2011
 Measure of tripartite entanglement in bosonic and fermionic systems
[Articolo su rivista]
F., Buscemi; Bordone, Paolo
abstract
We describe an efficient theoretical criterion suitable for the evaluation of the tripartite entanglement of any mixed threeboson or threefermion state, based on the notion of the entanglement of particles for bipartite systems of identical particles. Our approach allows one to quantify the accessible number of quantum correlations in the systems without any violation of the local particle number superselection rule. A generalization of the tripartite negativity is here applied to some correlated systems including the continuoustime quantum walks of identical particles (for both bosons and fermions) and compared with other criteria recently proposed in the literature. Our results show the dependence of the entanglement dynamics upon the quantum statistics: The bosonic bunching results in a low number of quantum correlations while FermiDirac statistics allows for higher values of the entanglement.
2011
 On demand entanglement in double quantum dots via coherent carrier scattering
[Articolo su rivista]
F., Buscemi; Bordone, Paolo; A., Bertoni
abstract
We show how two qubits encoded in the orbital states of two quantum dots can be entangled or disentangled in a controlled way through their interaction with a weak electron current. The transmission/reflection spectrum of each scattered electron, acting as an entanglement mediator between the dots, shows a signature of the dot–dot entangled state. Strikingly, while a few scattered carriers produce decoherence of the whole twodot system, a larger number of electrons injected from one lead with proper energy are able to recover its quantum coherence. Our numerical simulations are based on a realspace solution of the threeparticle Schrödinger equation with open boundaries. The computed transmission amplitudes are inserted in the analytical expression for the system density matrix to evaluate the entanglement.
2010
 Quantum teleportation of electrons in quantum wires with surface acoustic waves
[Articolo su rivista]
F., Buscemi; Bordone, Paolo; A., Bertoni
abstract
We propose and numerically simulate a semiconductor device based on coupled quantum wires, suitable for deterministic quantum teleportation of electrons trapped in the minima of surface acoustic waves. We exploit a network of interacting semiconductor quantum wires able to provide the universal set of gates for quantum information processing with the qubit defined by the localization of a single electron in one of two coupled channels. The numerical approach is based on a timedependent solution of the threeparticle Schrödinger equation. First, a maximally entangled pair of electrons is obtained via Coulomb interaction between carriers in different channels. Then, a complete Bellstate measurement involving one electron from this pair and a third electron is performed. Finally, the teleported state is reconstructed by means of local onequbit operations. The large estimated fidelity explicitly suggests that an efficient teleportation process could be reached in an experimental setup.
2009
 Dynamics of electron entanglement in semiconductor nanostructures
[Relazione in Atti di Convegno]
Bordone, Paolo
abstract
Quantum entanglement, the most remarkable feature of quantum physics, is recognized as a resource for quantum information processing. The quest for quantumcomputing devices has also produced great interest in entanglementformation in solidstate systems involving quantum effects. Indeed,the functionality of an increasing number of nanodevices is influenced by quantum correlations. In this work a theoretical approach developed in recent years to study the entanglement of fermions interacting via a Coulomb potential is presented, together with a number of applications to specific situations of physical interest in the field of charge transport in semiconductor nanostructures.
2009
 Dynamics of electronelectron entanglement in pulsed sinusoidal potentials
[Relazione in Atti di Convegno]
F., Buscemi; Bordone, Paolo; A., Bertoni
abstract
The surface acoustic wave (SAW) assisted charge transport represents a highly controllable mean to inject and drive electrons along quasi onedimensional channels. By means of a numerical approach, here we analyze the effect of the removal of SAW, for a finite time interval, onto the entanglement stemming from the Coulomb scattering between two charged carriers bound in SAW potential itself. We find that the particles get quickly entangled thus confirming that the SAW driven transport in lowdimensional semiconductor structures permits to suppress the effects of electronelectron correlation due to the Coulomb interaction.
2009
 Floquet projections of a Gaussian Wigner function in a KroningPenney potential
[Relazione in Atti di Convegno]
L., Maccari; L., Demeio; Bordone, Paolo
abstract
In this contribution, we apply the multiband model developed in \cite{ref3} to a KronigPenney potential and calculate the Floquet projections of a Gaussian Wigner function in phase space. The Bloch functions are calculated numerically and then used in the expressions of the Wigner projections.
2009
 Validity of the singleparticle approach for electron transport in quantum wires assisted by surface acoustic waves
[Articolo su rivista]
F., Buscemi; Bordone, Paolo; A., Bertoni
abstract
We study by means of timedependent numerical simulations the quantum entanglement stemming from the Coulomb interaction between two electrons trapped in the minima of the piezoelectric potential generated by surface acoustic waves. We find that for particles captured in lowenergy bound states the quantum correlations turn out to be negligible, thus validating a singleparticle approach to the dynamics of such systems. At long times, for highenergy electrons, a substantial entanglement appears, which is an indicator of a mostly correlated dynamics.
2008
 Effects of scattering resonances on carriercarrier entanglement in charged quantum dots
[Articolo su rivista]
F., Buscemi; Bordone, Paolo; A., Bertoni
abstract
We address the problem of the entanglement generationin an electronscattering by a 1D doublebarrier resonanttunnelling device. In particular we analyze the roleplayed by transport resonances in the appearance of quantumcorrelations between the energy states of the electrons.The entanglement is not sensitive to the presence of BreitWigner resonances, while it may be controlled by manipulatingFano resonances. Such a behavior is ascribed tothe different mechanisms characterizing the two types of processes.
2008
 Electron decoherence in a semiconductor due to electronphonon scattering
[Relazione in Atti di Convegno]
F., Buscemi; E., Cancellieri; Bordone, Paolo; A., Bertoni; Jacoboni, Carlo
abstract
In the present work we study, by means of numerical simulations, the coherent propagation of electrons in quantum wires and focus on the effect of the introduction of roughness along the channel. We study the electron evolution both in single and coupled quantum wires in the case where the electron freely move through the channel and in the case where transport is assisted by surface acoustic waves. It has been shown that systems of coupled quantum wires can realize a complete set of quantum logic gates.However, its physical implementation is severely limited by the spreading of the wave packet and by the presence of interface roughness. Our results show that the potential of the surface acoustic wave succeeds in confining the electron wavefunction and in driving it along the channels also when interface roughness is introduced. This suggests that electron transport assisted by surface acoustic waves could be a very efficient way to realize quantum solid state devices.
2008
 Roughness effect on electron transport through quantum wires
[Articolo su rivista]
E., Cancellieri; M., Rosini; Bordone, Paolo; Jacoboni, Carlo
abstract
In the present work we study, by means of numerical simulations, the coherent propagation of electrons in quantum wires and focus on the effect of the introduction of roughness along the channel. We study the electron evolution both in single and coupled quantum wires in the case where the electron freely move through the channel and in the case where transport is assisted by surface acoustic waves. It has been shown that systems of coupled quantum wires can realize a complete set of quantum logic gates.However, its physical implementation is severely limited by the spreading of the wave packet and by the presence of interface roughness. Our results show that the potential of the surface acoustic wave succeeds in confining the electron wavefunction and in driving it along the channels also when interface roughness is introduced. This suggests that electron transport assisted by surface acoustic waves could be a very efficient way to realize quantum solid state devices.
2008
 Simulation of decoherence in 1D systems, a comparison between distinguishable and indistinguishableparticle collisions
[Articolo su rivista]
F., Buscemi; Bordone, Paolo; A., Bertoni
abstract
We give a quantitative evaluation of the entanglement dynamics in scattering events between two electrons interacting via Coulomb potential in 1D systems, We apply a method, specifically designed for indistinguishable particles, based on the calculation of the von Neumann entropy of the system density matrix. From the timedependent numerical solution of the twoparticle wavefunction we evaluate the entanglement evolution for different spin configurations. The procedure allows to understand the mechanisms that govern entanglement creation and its connection with the characteristic physical parameters and initial conditions of the system.
2007
 Carriercarrier entanglement and transport resonances in semiconductor quantum dots
[Articolo su rivista]
F., Buscemi; Bordone, Paolo; A., Bertoni
abstract
We study theoretically the entanglement created in a scattering between an electron, incoming from a source lead, and another electron bound in the ground state of a quantum dot, connected to two leads. We analyze the role played by the different kinds of resonances in the transmission spectra and by the number of scattering channels, into the amount of quantum correlations between the two identical carriers. It is shown that the entanglement between their energy states is not sensitive to the presence of BreitWigner resonances, while it presents a peculiar behavior in correspondence to Fano peaks: two close maxima separated by a minimum for a twochannel scattering and a single maximum for a multichannel scattering. Such a behavior is ascribed to the different mechanisms characterizing the two types of resonances. Our results suggest that the production and detection of entanglement in quantum dot structures may be controlled by the manipulation of Fano resonances through external fields.
2007
 Effect of symmetry in the manyparticle Wigner funcion
[Articolo su rivista]
E., Cancellieri; Bordone, Paolo; Jacoboni, Carlo
abstract
An analysis of the Wigner function for identical particles is presented. Four situations have been considered. (i) The first is scattering process between two indistinguishable particles described by a minimum uncertainty wave packets showing the exchange and correlation effects in Wigner phase space. (ii) An equilibrium ensemble of N particles in a onedimensional box and in a onedimensional harmonic potential is considered second, showing that the reduced oneparticle Wigner function, as a function of the energy defined in the Wigner phase space, tends to the FermiDirac or to the BoseEinstein distribution function, depending on the considered statistics. (iii) The third situation is reduced oneparticle transport equation for the Wigner function, in the case of interacting particles, showing the need for the twoparticle reduced Wigner function within the BogoliubovBornGreenKirkwoodYvon hierarchy scheme. (iv) Finally, the electronphonon interaction in the twoparticle case is considered, showing coparticipation of two electrons in the interaction with the phonon bath.
2007
 Entanglement Creation for TwoElectron Scattering in a 2D System
[Articolo su rivista]
F., Buscemi; Bordone, Paolo; A., Bertoni
abstract
Recently great attention has been addressed to the study of quantum correlations in systems of identical particles. Various definitions of entanglement for indistinguishable particles are present in the literature. Following Schliemann’s theory, here we perform a quantitative evaluation of the entanglement dynamics for electronelectron scattering in a 2D system in terms of the von Neumann entropy of the reduced oneparticle density matrix. Our approach allows us to define the time of entanglement formation and to investigate the role of the space and spin degrees of freedom in the building up of quantum correlations.
2007
 Linear entropy as an entanglement measure in twofermion systems
[Articolo su rivista]
F., Buscemi; Bordone, Paolo; A., Bertoni
abstract
We describe an efficient theoretical criterion, suitable for indistinguishable particles to quantify the quantum correlations of any pure twofermion state, based on the Slater rank concept. It represents the natural generalization of the linear entropy used to treat quantum entanglement in systems of nonidentical particles. Such a criterion is here applied to an electronelectron scattering in a twodimensional system in order to perform a quantitative evaluation of the entanglement dynamics for various spin configurations and to compare the linear entropy with alternative approaches. Our numerical results show the dependence of the entanglement evolution upon the initial state of the system and its spin components. The differences with previous analyses accomplished by using the von Neumann entropy are discussed. The evaluation of the entanglement dynamics in terms of the linear entropy results to be much less demanding from the computational point of view, not requiring the diagonalization of the density matrix.
2007
 Simulation of the entanglement creation for identical particles scattering in a 2D system
[Articolo su rivista]
F., Buscemi; Bordone, Paolo; A., Bertoni
abstract
In recent years the dynamics of entanglement formation between two distinguishable charged particles has been investigated for scattering events in bulk semiconductors. The aim of this work is to overcome the hypothesis of distinguishable carriers. Here we present a quantitative evaluation of the entanglement dynamics for electronelectron collisions in a 2D system applying a method, suitable for indistinguishable particles, based on the Slater rank and the von Neumann entropy of the reduced density matrix. The quantum entanglement of both spatial and spin degrees of freedom is computed for various initial conditions of the system.
2006
 Electron dynamics inside shortcoherence systems
[Articolo su rivista]
G., Ferrari; Bordone, Paolo; Jacoboni, Carlo
abstract
We present theoretical results on electron dynamics inside nanometric systems, where the coherence of the electron ensemble is maintained in a very short region. The contacts are supposed to spoil such a coherence, therefore the interference processes between the carrier wavefunction and the internal potential profile can be affected by the proximity of the contacts. The problem has been analysed by using the Wignerfunction formalism. For very short devices, transport properties, such as tunnelling through potential barriers, are significantly influenced by the distance between the contacts.
2006
 Entanglement dynamics of electronelectron scattering in lowdimensional semiconductor systems
[Articolo su rivista]
F., Buscemi; Bordone, Paolo; A., Bertoni
abstract
We perform the quantitative evaluation of the entanglement dynamics in scattering events between two indistinguishable electrons interacting via the Coulomb potential in one and twodimensional semiconductor nanostructures. We apply a criterion based on the von Neumann entropy and the Schmidt decomposition of the global state vector suitable for systems of identical particles. From the timedependent numerical solution of the twoparticle wave function of the scattering carriers we compute their entanglement evolution for different spin configurations: two electrons with the same spin, with different spin, and singlet and triplet spin states. The procedure allows us to evaluate the mechanisms that govern entanglement creation and their connection with the characteristic physical parameters and initial conditions of the system. The cases in which the evolution of entanglement is similar to the one obtained for distinguishable particles are discussed.
2006
 Exchange effects in the Wignerfunction approach
[Relazione in Atti di Convegno]
E., Cancellieri; Bordone, Paolo; Jacoboni, Carlo
abstract
In this paper, an analysis of the Wigner function (WF) for identical fermions is presented. Three situations have been analyzed. i) A scattering process between two indistinguishable electrons in minimum uncertainty wavepackets showing the exchange and correlation hole in Wigner phase space. ii) An equilibrium ensemble of N electrons in a box showing that the WF integrated over space assumes the shape of a Fermi distribution even for very small N. iii) The reduced oneparticle transportequation for the WF in the case of interacting electrons showing the first contribution to the BBGKY hierarchy.
2006
 Quantum phononlimited highfield electron transport in semiconductors
[Relazione in Atti di Convegno]
Ferrari, G; Cancellieri, E; Bordone, Paolo; Jacoboni, Carlo
abstract
A fully quantum theory of phononlimited electron transport in semiconductors is applied to a homogeneous steadystate situation to investigate the difference between quantum results and the results of a semiclassical theory. The Wigner function is used for the quantum approach, and the Monte Carlo simulations are performed in both semiclassical and quantum theories. In the considered case, hotelectron transport in a simple silicon model at 77 K, very little difference has been found since collisional broadening changes the possible final states of the electronic transitions without altering in a significan way the total scattering rate and therefore the momentum relaxation efficiency of phonon scattering.
2006
 Simulation of entanglement creation for carrierimpurity scattering in a 2D system
[Relazione in Atti di Convegno]
Bordone, Paolo; Bertoni, A.
abstract
We present a time dependent numerical analysis of the entanglment created between an electron freely propagating in a 2D system and a charged particle bound to a specific site by a harmonic potential. The latter can be considered as a simplified model of a shallow impurity. The dynamics of the carrier initially bound in the harmonic potential is coupled to that of the incoming electron through a screened Coulomb interaction. The entanglement is found to depend significantly on the energy of the freely propagating particle, on the confinig energy of the harmonic potential and on the sign of the charge bound by the harmonic potential. This approach allows a quantitative estimate of the decoherence undergone by propagating carrier due to a single unelastic scattering.
2005
 Multiband, nonparabolic Wignerfunction approach to electron transport in semiconductors
[Articolo su rivista]
L., Demeio; Bordone, Paolo; Jacoboni, Carlo
abstract
In this work, we introduce a multiband transport model for quantum electron transport in semiconductors following the Wignerfunction approach. By using the BlochFloquet decomposition of the density matrix, we obtain the BlochFloquet projections of the Wigner function and derive their evolution equations for energy bands of arbitrary shape. The equations of the model are very general and allow (in principle) the investigation of quantum processes in which interband transitions and/or nonparabolicity effects may occur. Finally, we present numerical applications for some particular cases in which the numerical solution can be obtained easily.
2004
 30 years of HCIS
[Articolo su rivista]
Jacoboni, Carlo; Bordone, Paolo
abstract
On the occasion of the 30th anniversary of the HCIS conference, we would like to provide a general, although necessarily not exhaustive, picture of how the conference has changed over the years and of how the natural evolution of research has influenced its various editions. By performing a statistical analysis of specific sets of data, we try to identify some characteristic trends that, we believe, can contribute to a better understanding of how our field of research has been developing in the last three decades. On request of the editor, we added the data relative to HCIS13.
2004
 Coherent transport in coupled quantum wires assisted by surface acoustic waves
[Articolo su rivista]
Bordone, Paolo; A., Bertoni; M., Rosini; S., Reggiani; Jacoboni, Carlo
abstract
In this work we present a simulation of the coherent evolution of electrons in two coupled quantum wires assisted by surface acoustic waves. The system under study has recently been proposed as a model for a solidstate realization of quantum gates. A quantum NOT transformation and an electron beam splitter have been numerically simulated. Results show that the surface acoustic waves improve the functionality of the device by preventing the spreading of the electron wavefunction and reducing undesired reflection effects.
2004
 Influence of contacts on the electron transport dynamics inside a mesoscopic system
[Articolo su rivista]
G., Ferrari; N., Giacobbi; Bordone, Paolo; Jacoboni, Carlo; A., Bertoni
abstract
In mesoscopic systems the Wigner function picture is used for studying electron quantum transport. In this work we present theoretical results on the effect of contact proximity in nanometric devices. If the correlation of the electron wavefunction vanishes inside the contact regions, the transport properties inside the device are affected. We have verified this influence analytically. The main effect is the dependence of the tunnel current through potential barriers on the distance between the contacts. Using three different simulation schemes we have observed modifications in the electron density and conductance for simple devices depending on the distance between the contacts.
2004
 Nonparabolic electron transport in semiconductors by the Wignerfunction approach
[Abstract in Atti di Convegno]
L., Demeio; Bordone, Paolo; G., Frosali
abstract
The Wigner function approach to electron transport in semiconductors is commonly used to describe the properties of electronic devices. Until now, this approach was restricted to the description of the conduction band electrons, under the effectivemass approximation. A multiband, nonparabolic transport model has been introduced; numerical results for multiband transport have been obtained until now only for very elementary examples and more extensive numerical work is underway; numerical results for nonparabolic, singleband transport have been more numerous and easier to obtain, so this aspect has been studied in more detail. We shall illustrate some of the results in this symposium.
2004
 Numerical simulation of an intervalley transition by the Wignerfunction approach
[Articolo su rivista]
L., Demeio; Bordone, Paolo; Jacoboni, Carlo
abstract
In this work we present a recently developed transport model, based on the Wignerfunction approach and allowing for nonparabolic band profiles. Two scattering mechanismIs are included by means of a Boltzmannlike collision operator, describing the collisions between electrons and polar optical and intervalley phonons. The transport equation for the Wigner function is solved by the splittingscheme algorithm. We have chosen a onedimensional model band profile, which exhibits satellite valleys, besides the minimum at the centre of the Brillouin zone, similar to the band profile of GaAs.
2004
 Preface: Special issue featuring papers from the International Conference on Nonequilibrium Carrier Dynamics in Semiconductors
[Relazione in Atti di Convegno]
Reggiani, L.; Bordone, P.; Brunetti, R.
abstract
2004
 Semiconductor Science and Technology  Special issue featuring papers from the International Conference on Nonequilibrium Carrier Dynamics in Semiconductors
[Curatela]
L., Reggiani; Bordone, Paolo; Brunetti, Rossella
abstract
Proceedings of the 13th International Conference on Nonequilibrium Carrier Dynamics in Semiconductors. The volume addresses eleven major topics: carrier transport in low dimensional and nanostructure systems, noneuillibrium carriers in superlattices and devices, small devices and related phanomena, carrier dynamics and fluctuations, carrier quantum dynamics, coherent/incoherent carrier dynamics of optical excitations and ultrafast optical phenomena, nonlinear optical effects, transport in organic matter, semiconductorbased spitronics, coherent dynamics in solid state systems for quantum processing and communications, novel materials and devices.
2004
 Simulation of entanglement dynamics for a scattering between a free and a bound carrier in a quantum wire
[Articolo su rivista]
Bordone, Paolo; A., Bertoni; Jacoboni, Carlo
abstract
The decoherence of a quantum system is ascribed to its enetanglement with another system considered as the environment, thus the quantitative evaluation of entanglement formation dynamics can shed light on the transition between quantum and classical behavior of a carrier that undergoes to a scattering event. We present here a numerical solution of the timedependent 1D Schroedinger equation of a twoparticle system consisting of a free carrier scattered by a bound one. The realspace entanglement between them is computed, at different times, for various initial conditions. The maximum entanglement corresponds to equal probability of transmission and reflection of the free particle.
2004
 Single electron transport and entanglement induced by surface acoustic waves versus free ballistic propagation in coupled quantum wires
[Articolo su rivista]
M., Rosini; A., Bertoni; Bordone, Paolo; Jacoboni, Carlo
abstract
In this work we study the coherent propagation of electrons in quantum wires driven by surface acoustic waves, as a part of a feasibility study on a coupled quantum wires device, able to realize the basic operations needed for quantum computing. We demonstrate that the introduction of the surface acoustic wave is able to improve the devices performance. In particular, single and doublequbit quantum gates have been simulated and better results are obtained, with respect to the free electron propagation. A further analysis reveals a strong reduction of the final undesired spatial entanglement and confirms the effectiveness of the dynamics driven by surface acoustic wave.
2004
 The Wignerfunction approach to nonequilibrium electron transport
[Articolo su rivista]
Jacoboni, Carlo; Bordone, Paolo
abstract
The Wignerfunction (WF) approach to quantum electron transport in semiconductors is reviewed in this paper. The main definitions and properties related to the WF are presented, with a discussion of the various forms of the dynamical equations that govern its evolution. Monte Carlo solutions of such equations are also discussed. Interactions of electrons with applied fields, potential profiles, and phonons are analysed in detail. Finally, several physical applications are presented. Each topic has been developed from basic principles for the benefit of interested readers who are not experts in the particular subjects discussed in this paper.
2004
 Wigner functions for identical particles
[Articolo su rivista]
E., Cancellieri; Bordone, Paolo; A., Bertoni; G., Ferrari; Jacoboni, Carlo
abstract
In this work the Wigner function approach to quantum transport developed for the single electron case is extended to a more complicated system for n indistingushable particles. In particular we study how the Monte Carlo tecnique and the Wigner paths method can be applyed to a single particle Wigner function defined for a system of n interacting particles. The numerical results are obtained for the case of a system of two particles under different conditions: two noninteracting fermions, two noninteracting bosons, two non interacting distinguishable particles and two interacting fermions.
2003
 Dinamica elettronica in sistemi mesoscopici
[Abstract in Atti di Convegno]
Bordone, Paolo; Jacoboni, Carlo
abstract
Negli ultimi anni, la continua riduzione delle dimensioni dei dispositivi a semiconduttore ha reso chiaro quanto sia necessario un approccio quantistico al problema del trasporto di carica. Il metodo, basato sul formalismo della funzione di Wigner si e` mostrato particolarmente adatto a questo scopo, sia per l'analogia formale con la descrizione classica in termini di spazio delle fasi, sia per il naturale utilizzo delle condizioni al contorno. Tra i risultati principali fin' ora ottenuti si ha una possibile spiegazione della sorprendente attendibilita` dell'approccio semiclassico (equazione di Boltzmann) e l'influenza della distanza dei contatti sulla dinamica elettronica interna ad un sistema mesoscopico.
2003
 Monte Carlo simulation of quantum electron transport based on Wigner paths
[Articolo su rivista]
Bordone, Paolo; A., Bertoni; Brunetti, Rossella; Jacoboni, Carlo
abstract
Advancements and improvements in the Wigner function approach to quantum electron transport are reviewed. The concept of Wigner paths allows the formulation of the Monte Carlo simulation in strict analogy with the one used in semiclassical transport theory.
2003
 NUMERICAL AND ANALYTICAL APPLICATIONS OF MULTIBAND TRANSPORT IN SEMICONDUCTORS
[Relazione in Atti di Convegno]
L., Demeio; Bordone, Paolo; Jacoboni, Carlo
abstract
A multiband transport model for electron transport in semiconductors, based on the Wignertransport approach and allowing for energy bands of arbitrary shape, is presented and applied to two simple examples: a comparison of exact and free streaming solutions of teh Wigner equation in nonparabolic regime and an interband transition in an infinite homogeneous medium.
2003
 PROXIMITY EFFECT OF THE CONTACTS ON ELECTRON TRANSPORT IN MESOSCOPIC DEVICES
[Articolo su rivista]
A., Bertoni; Bordone, Paolo; G., Ferrari; N., Giacobbi; Jacoboni, Carlo
abstract
The Wigner function formalism is used for studying electron quantum transport in mesoscopic systems. In this work we show that, if the correlation of the electron wave function vanishes outside the region of interest (for example inside the contacts), then transport is affected inside the device. This property is verified analytically. Results show that, for very short devices, tunneling is actually influenced by the distance between the contacts. Modification in the electron density and conductivity have been numerically observed.
2003
 Wigner function for multiband transport in semiconductors
[Articolo su rivista]
L., Demeio; L., Barletti; Bordone, Paolo; Jacoboni, Carlo
abstract
In this work we present a onedimensional model of quantum electron transport in semiconductors that makes use of the Wigner function formalism and that takes into account the full band structure of the medium for energy bands of any shape. We introduce a multiband Wigner function and derive the evolution equations for each component, with and without external fields, by using a Bloch states representation of the density matrix.
2003
 Wignerpath approach to nonequilibrium quantum transport
[Relazione in Atti di Convegno]
Jacoboni, Carlo; Bordone, Paolo; Brunetti, Rossella
abstract
Recent developments of the application of the Wignerpath method to nonequilibrium quantum transport in mesoscopic systems are presented. The concept of wigner path allows the formulation of a Monte Carlo simulation which is quantum mechanically rigorous and yet very similar to the one used in semiclassical transport theory. Scatterings with the potential profile and with phonons are included in the path in a way that takes automatically into account all quantum effects, such as intracollisional field effect and collisional broadening.
2002
 Infinite barriers and classical force in the Wignerfunction approach to quantum electron transport
[Articolo su rivista]
Bordone, Paolo; A., Bertoni; Jacoboni, Carlo
abstract
In this paper some advancements in the development of the Wignerfunction approach to quantum electron transport are presented. In particular we reexamined the problem of the interaction of the carriers with a potential profile with the purpose of isolating relevant differences with respect to classical dynamics. In order to simplify the notation phonon scattering has not been included. In particular, two cases are considered: (1) infinite potential barriers, and (2) the separation of the classical force from the quantum contributions in a general potential profile. (C) 2002 Elsevier Science B.V. All rights reserved.
2002
 Numerical simulation of coherent transport in quantum wires for quantum computing
[Articolo su rivista]
A., Bertoni; Bordone, Paolo; Brunetti, Rossella; Jacoboni, Carlo; S., Reggiani
abstract
A solidstate implementation of a universal set of gates for quantum computation is proposed and analysed using a timedependent 2D Schrodinger solver. The qubit is defined as the state of an electron propagating along a couple of quantum wires. The wires are suitably coupled through a potential barrier with variable height and/or width. It is shown how a proper design of the system allows the implementation of any onequbit transformation. The twoqubit gate is realized through a Coulomb coupler able to entangle the quantum states of two electrons running in two wires of two different qubits. The simulated devices are GaAsAlGaAs heterostructures that should be on the borderline of present semiconductor technology. An estimate of decoherence effects due to phonon scattering is also presented.
2002
 Wigner Paths for Quantum Transport
[Articolo su rivista]
Bordone, Paolo; Jacoboni, Carlo
abstract
A Monte Carlo algorithm based on the concept of Wigner paths has been developed to study quantum transport in mesoscopic systems in strict analogy with the traditional Monte Carlo simulation used to solve the Boltzmann transport equation. Scatterings with both phonons and impurities can be accounted for. As regards a structure potential profile the effect of the corresponding classical force can be inserted in the dynamics of the free flight, while quantum effects due to rapid potential variations are included as a special scattering mechanism.
2002
 Wignerfunction approach to multiband transport in semiconductors
[Articolo su rivista]
L., Demeio; L., Barletti; A., Bertoni; Bordone, Paolo; Jacoboni, Carlo
abstract
In this work we present a onedimensional, multiband model for electron transport in semiconductors that makes use of the Wignerfunction formalism and that allows for energy bands of any shape. A simplified twoband model is then derived from the general equations, by using the parabolic band approximation.
2001
 DYNAMICAL EQUATION AND MONTE CARLO SIMULATION OF THE TWOTIME WIGNER FUNCTION FOR ELECTRON QUANTUM TRANSPORT
[Articolo su rivista]
Brunetti, Rossella; A., Bertoni; Bordone, Paolo; Jacoboni, Carlo
abstract
Within the Wignerfunction formalism for electron quantum transport in semiconductors a twotime Wigner function is defined starting from the Greenfunction formalism. After a proper Fourier transform a Wigner function depending on p and W as independent variables is obtained. This new Wigner function extends the Wigner formalism to the frequency domain and carries information related to the spectral density of the system. A Monte Carlo approach based on the generation of Wigner paths, already developed for the singletime Wigner function, has been extended to evaluate the momentum and energydependent Wigner function. Results will be shown for electrons subject to the action of an external field and in presence of scattering with optical phonons.
2001
 Numerical simulation of quantum logic gates based on quantum wires
[Articolo su rivista]
Bertoni, A; Bordone, Paolo; Brunetti, Rossella; Jacoboni, Carlo; Reggiani, S.
abstract
A system based on frontier mesoscopic semiconductor technology, able to perform the basic quantum operations needed for quantum computation, is proposed. The elementary quantum bit (qubit) is defined as the state of an electron running along a couple of quantum wires coupled through a potential barrier with variable height and/or width. A proper design of the system, together with the action of Coulomb interaction of two electrons representing two different qubits, allows the implementation of basic onequbit and twoqubit quantum logic gates. Numerical simulations confirm the correctness of the hypothesis.
2001
 Quantum transport and its simulation with the Wignerfunction approach
[Capitolo/Saggio]
Jacoboni, Carlo; Brunetti, Rossella; Bordone, Paolo; A., Bertoni
abstract
In this paper a review of the research performed in recent years by the group of the authors is presented. The definition and basic properties of the Wigner function are first given. Several forms of its dynamical equation are then derived with the inclusion of potential and phonon scattering. For the case of a potential V(r) the effect of the classical force, for any form of V(r), is separated from quantum effects due to rapidly varying potentials. An elaboration of the dynamical equation is introduced that leads to Wigner paths formed by free flights and scattering events. These are especially suitable for a Monte Carlo solution of the transport equation for the Wigner function very similar to the semiclassical traditional Monte Carlo simulation. The Monte Carlo simulation can be extended also to the momentum and frequency dependent Wigner function based on a twotime Green function. Several numerical results are presented throuhout the paper.
2001
 Wigner Paths Method in Quantum Transport with Dissipation
[Articolo su rivista]
Bordone, Paolo; A., Bertoni; Brunetti, Rossella; Jacoboni, Carlo
abstract
The concept of Wigner paths in phase space both provides a pictorial representation of the quantum evolution of the system of interest and constitutes a useful tool for numerical solutions of the quantum equation describing the time evolution of the system. A Wigner path is defined as the path followed by a “simulative particle” carrying a σcontribution of the Wigner function through the Wigner phasespace, and is formed by ballistic free flights separated by scattering processes (both scattering with phonons and with an arbitrary potential profile can be included), as for the case of semiclassical particles. Thus, the integral transport equation can be solved by a Monte Carlo technique by means of simulative particles following classical trajectories, in complete analogy to the “Weighted Monte Carlo” solution of the Boltzmann equation in the integral form.
2001
 Wignerfunction formulation for quantum transport in semiconductors: theory and Monte Carlo approach
[Articolo su rivista]
Jacoboni, Carlo; A., Bertoni; Bordone, Paolo; Brunetti, Rossella
abstract
The Wignerfunction approach to the quantum theory of electron transport in mesoscopic systems is reviewed. Deltalike or particle contributions to the Wigner function evolve in time along paths formed by ballistic free flights interrupted by scattering processes as semiclassical particles. A Monte Carlo algorithm based on such Wigner paths will be presented. It extends to quantum transport the Monte Carlo procedure that proved to be very successful for the study of semiclassical transport. (C) 2001 IMACS. Published by Elsevier Science B.V. All rights reserved.
2000
 Quantum logic gates based on coherent electron transport in quantum wires
[Articolo su rivista]
A., Bertoni; Bordone, Paolo; Brunetti, Rossella; Jacoboni, Carlo; S., Reggiani
abstract
It is shown that the universal set of quantum logic gates can be realized using solidstate quantum bits based on coherent electron transport in quantum wires. The elementary quantum bits are realized with a proper design of two quantum wires coupled through a potential barrier Numerical simulations show that (a) a proper design of the coupling barrier allows one to realize any oneqbit rotation and (b) Coulomb interaction between two qbits of this kind allows the implementation of the CNOT gate. These systems are based on a mature technology and seem to be integrable with conventional electronics.
2000
 TWOQBIT GATES BASED ON COUPLED QUANTUM WIRES
[Relazione in Atti di Convegno]
S., Reggiani; A., Bertoni; Bordone, Paolo; Brunetti, Rossella; Jacoboni, Carlo; M., Rudan; G., Baccarani
abstract
A solidstate implementation of a set of one and twoqbit gates for quantum computing is proposed. the qbit is defined as the state of an electron running along two quantum wires, suitably coupled through a potential barrier with variable height and/or width. Singlequbit gates are implemented using the coupling between the two wires. The twoqbit gates have been designed using a Coulomb coupler to induce a mutual phase modulation of the two qubits. A number of runs have been perfomed using a timedependent 2D Schroedinger solver.
1999
 Quantum transport of electrons in open nanostructures with the Wignerfunction formalism
[Articolo su rivista]
Bordone, Paolo; M., Pascoli; Brunetti, Rossella; A., Bertoni; Jacoboni, Carlo; A., Abramo
abstract
A theoretical Wignerfunction approach to the study of quantum transport in open systems in presence of phonon scattering is presented. It is shown here that in order to solve the Wigner equation in its integral form the knowledge of the Wigner function at all points of the phase space at an initial time t0 can be substituted by the knowledge of the same function inside the region of interest at t0 and on its boundary at all times t′ less then the observation time t. The theory has been applied to calculate the current associated with electron quantum transport across given potential profiles and in presence of phonon scattering.
1999
 Quantum versus classical scattering in semiconductor charge transport: a quantitative comparison
[Articolo su rivista]
A., Bertoni; Bordone, Paolo; Brunetti, Rossella; Jacoboni, Carlo; N., Sano
abstract
A firstprinciple analysis is presented of the effect on transport phenomena of the relaxation of the semiclassical assumptions of energy conservation and pointlike nature in space/time of the scattering processes. Quantitative estimates for the quantum case have been obtained within the Wignerfunction approach with the use of the concept of Wigner paths. This formulation of the transport problem, although rigorous from the point of view of quantum mechanics, is very close to the classical language, so that comparisons are very straightforward. Results of the analysis of phonon scattering show that multiple collisions reduce collisional broadening and contribute to understanding the success of the semiclassical approximation. An analogous formulation in terms of the density matrix confirms the obtained results. (C) 1999 Elsevier Science B.V. All rights reserved.
1999
 THE WIGNER FUNCTION FOR ELECTRON TRANSPORT IN MESOSCOPIC SYSTEMS
[Articolo su rivista]
A., Bertoni; Bordone, Paolo; Brunetti, Rossella; Jacoboni, Carlo
abstract
The Wignerfunction approach to the quantum theory of electron transport in mesoscopic systems is reviewed. Deltalike or 'particle' contributions to the Wigner function are introduced that evolve in time along 'paths' formed by ballistic free Eights separated by scattering processes like semiclassical particles. A Monte Carlo algorithm can be developed, based on such Wigner paths. Furthermore, a twotime Green function G can be used to define a Wigner function where momentum and energy are treated as independent variables. The same Monte Carlo approach would then also yield the spectral function for the electron interacting with the phonon gas.
1999
 WIGNER PATHS FOR QUANTUM TRANSPORT IN SEMICONDUCTORS
[Relazione in Atti di Convegno]
Bordone, Paolo; Brunetti, Rossella; M., Pascoli; A., Bertoni; Jacoboni, Carlo
abstract
Wigner paths in phase space associated with electronic quantum transport in the Wignerfunction formulation are presented and compared with Wigner trajectories, already used in the literature for the case of ballistic coherent transport. Furthermore it is indicated how Wigner paths can be profitably used for the numerical study of quantum transport in mesoscopic systems in presence of phonon scattering.
1998
 APPLICATION OF THE WIGNERFUNCTION FORMULATION TO MESOSCOPIC SYSTEMS IN PRESENCE OF ELECTRONPHONON INTERACTION
[Articolo su rivista]
Jacoboni, Carlo; A., Abramo; Bordone, Paolo; Brunetti, Rossella; M., Pascoli
abstract
A theoretical and computational analysis of the quantum dynamics in presence of electronphonon interaction based on the Wigner function is here applied to the study of transport in mesoscopic systems. Numerical applications are shown for a) a wavepacket scattering with phonons while crossing a potential profile and b) electrons scattering with phonons in a finite device with open boundary conditions.
1998
 MONTE CARLO SIMULATION OF SEMICONDUCTOR TRANSPORT
[Capitolo/Saggio]
Jacoboni, Carlo; Brunetti, Rossella; Bordone, Paolo
abstract
The contribution is mainly related to advanced problems in Monte Carlo simulations. The first section is concerned with physical models. The fundamentals of the method are discussed in next section. Then the chapter deals with applications and results for bulk semiconductor systems, low dimensional structures and devices.
1998
 QUANTUM ELECTRONPHONON INTERACTION FOR TRANSPORT IN OPEN NANOSTRUCTURES
[Relazione in Atti di Convegno]
Bordone, Paolo; Brunetti, Rossella; M., Pascoli; Jacoboni, Carlo
abstract
Electronic quantum transport accounting for coherent propagation and electronphonon scattering has been used to calculate the currentvoltage characteristics for model nanostructures.
1998
 Quantum transport simulation of the DOS function, selfconsistent fields and mobility in MOS inversion layers
[Articolo su rivista]
Vasileska, D; Eldridge, T; Bordone, Paolo; Ferry, Dk
abstract
We describe a simulation of the selfconsistent fields and mobility in (100) Siinversion layers for arbitrary inversion charge densities and temperatures. A nonequilibrium Green's functions formalism is employed for the state broadening and conductivity. The subband structure of the inversion layer electrons is calculated selfconsistently by simultaneously solving the Schrodinger, Poisson and Dyson equations, The selfenergy contributions from the various scattering mechanisms are calculated within the selfconsistent Born approximation. Screening is treated within RPA, Simulation results suggest that the proposed theoretical model gives mobilities which are in excellent agreement with the experimental data.
1998
 WIGNER PATHS AND BOUNDARY CONDITIONS FOR ELECTRON TRANSPORT IN OPEN SYSTEMS WITH ELECTRONPHONON INTERACTION
[Relazione in Atti di Convegno]
Jacoboni, Carlo; A., Bertoni; Bordone, Paolo; Brunetti, Rossella
abstract
Ed.IEEE, CAT.N.98X116
1998
 WIGNER PATHS AND BOUNDARY CONDITIONS FOR ELECTRON TRANSPORT IN OPEN SYSTEMS WITH ELECTRONPHONON INTERACTION
[Relazione in Atti di Convegno]
Jacoboni, Carlo; A., Bertoni; Bordone, Paolo; Brunetti, Rossella
abstract
A Wignerfunction approach to the study of quantum transport in open systems in presence of phonon scattering is presented. Two important issues will be discussed in the paper: a) the existence of Wigner paths in phase space with many analogies with the semiclassical description of transport and b) how to deal with boundary conditions for the analysis of real open structures. Theoretical and computational results will be discussed in view of the application of this formalism to the simulation of transport in mesoscopic structures.
1998
 Wigner paths for electrons interacting with phonons
[Articolo su rivista]
M., Pascoli; Bordone, Paolo; Brunetti, Rossella; Jacoboni, Carlo
abstract
Wigner trajectories in phase space provide a pictorial representation of the quantum evolution of a system of interest in the Wignerfunction formulation of quantum mechanics with many analogies with the description of classical evolutions. The existence of Wigner trajectories has been discussed so far only for ballistic coherent electrons moving in an external potential profile. We prove in this paper the existence of Wigner paths that are defined also in the presence of electronphonon coupling, and go over some interpretative problems related to Wigner trajectories. Wigner paths can be used to determine the evolution of the Wigner function in time during scattering processes. This general result opens new fields of application of the concept of Wigner function, mainly in connection with the numerical study of quantum transport in mesoscopic systems.
1997
 Using the Wigner function for quantum transport in device simulation
[Articolo su rivista]
M., Nedjalkov; I., Dimov; Bordone, Paolo; Brunetti, Rossella; Jacoboni, Carlo
abstract
The Wigner function was introduced as a generalization of the concept of distribution function for quantum statistics. The aim of this work is pushing further the formal analogy between quantum and classical approaches. The Wigner function is defined as an ensemble average, i.e., in terms of a mixture of pure states. From the point of view of basic physics, it would be very appealing to be able to define a Wigner function also for pure states and the associated expectation values for quantum observables, in strict analogy with the definition of mean value of a physical quantity in classical mechanics; then correct results for any quantum system should be recovered as appropriate superpositions of such ''purestate'' quantities. We will show that this is actually possible, st the cost of dealing with generalized functions in place of proper functions.
1997
 Wigner function for open systems with electronphonon interaction
[Articolo su rivista]
Bordone, Paolo; A., Abramo; Brunetti, Rossella; M., Pascoli; Jacoboni, Carlo
abstract
The Wignerfunction (WF) formalism is used to analyze the quantum dynamics of charge carriers in presence of electronphonon (ep) interaction in open mesoscopic systems making use of the perturbation theory with the external fields incorporated into the unperturbed Hamiltonian. Proper boundary conditions have been chosen and the transport phenomenon inside the device is treated in such a way that boundary conditions at finite positions are kept unaltered, even though the basis of extended scattering states is used.
1996
 Collision duration for polar optical and intervalley phonon scattering
[Relazione in Atti di Convegno]
Bordone, Paolo; D., Vasileska; D. K., Ferry
abstract
The use of fs laser pulses to excite plasmas in semiconductors has become a major method for studying fast processes. The transition times from the Gamma valley to the satellite X and L valleys are comparable to the reciprocal of the frequency of the phonons involved, bringing into question the use of the standard perturbationtheory approaches. Our aim is to evaluate the time required to emit a phonon, either the intravalley LO or the intervalley, by a nearlyfree electron in semiconductors. The leading idea of our work is that the socalled ''collision duration'' is related to the time required to build up correlation between the initial and final state, and then to destroy this correlation as the collision is completed. The calculations are developed using e nonequilibrium Green's function formalism, which allows us to evaluate explicitly the effects of the correlations in time.
1996
 Collision duration time for optical phonon emission in semiconductors
[Articolo su rivista]
Bordone, Paolo; D., Vasileska; D. K., Ferry
abstract
The time required to emit an optical (polar and intervalley) phonon by a nearlyfree electron in a semiconductor is evaluated using a nonequilibrium Green'sfunction formalism. The leading idea of the work is that the socalled "collision duration" is related to the time required to build up correlation between the initial and the final state, and then to destroy this correlation as the collision is completed. The use of the nonequilibrium Green'sfunction formalism gives us the possibility to evaluate explicitly the effects of the correlations in time. Our approach is based on two crucial assumptions: we build the selfenergy from only the polarization field of the polaroptical phonon; that is, the selfenergy is a function of a single time and position, and we introduce the electron correlation function between the initial and the final states, written in terms of a generalized lessthan Green's function in the momentum variables. We derive an analytical expression for the probability for a carrier to end up in a final state k as a consequence of the emission of a phonon as a function of time. We find that the probability rises to the "Fermi golden rule" result within a few femtoseconds. If the total lifetime broadening of the initial state is comparable to the scattering time, the probability oscillates as it approaches the asymptotic value. For larger initialstate broadening (due to more scattering processes), these oscillations disappear.
1996
 Quantum transport calculations for silicon inversion layers in MOS structures
[Articolo su rivista]
Vasileska, D; Bordone, Paolo; Eldridge, T; Ferry, Dk
abstract
We evaluate the mobility of inversion layer electrons in silicon MOSFETs using a realtime Green's functions formalism. Simulation results suggest that interfaceroughness considerably affects the lowheld mobility, even at room temperature. We also find that an exponential model for the surfaceroughness autocorrelation function, as well as Ando's model for the surfaceroughness matrix element, leads to the best description of this scattering process over a wide range of inversion charge densities and temperatures. Universal mobility behavior is observed when the proper weighting coefficient for the depletion charge density is used in the definition of the effective field.
1995
 Calculation of the average interface field in inversion layers using zerotemperature Green's function formalism
[Articolo su rivista]
D., Vasileska Kafedziska; Bordone, Paolo; T., Eldridge; D. K., Ferry
abstract
We investigate the dependence of the average interface field on the inversion and depletion charge density through the use of a zerotemperature Green's function formalism for the evaluation of the broadening of the electronic states and conductivity. Various models for the surfaceroughness autocovariance function existing in the literature, including both Gaussian and exponential models, are studied in our calculations. Besides surfaceroughness scattering, the dominant scattering mechanism at high electron densities, charged impurity, interfacetrap and oxide charge scattering are also included. The position of the subband minima, as well as the electron wave functions, are obtained by a selfconsistent solution of the Schrödinger, Poisson, and Dyson equations for each value of the inversion charge density. Manybody effects are included by considering the screened matrix elements for the scattering mechanisms and through inclusion of the exchangecorrelation term. The dependence of the mobility and the effective field upon the inversion charge density is sensitive to the model chosen, and we discuss the manner in which this may be used to study the interface itself.
1995
 Evaluation of the mobility in a SiSiO2 inversion layer at T=0 using Greeen's function formalism
[Relazione in Atti di Convegno]
D., Vasilaska; Bordone, Paolo; T., Eldrirge; D. K., Ferry
abstract
The transport properties of lowdimensional systems, such as inversion layers, quantum wells, heterostructures and superlattices, have been a focus of scientific research for many years, but more so recently due to the advances in the miscrofabrication of metallic and semiconductors nanostructures. In these structures, the motion of the electrons in the direction perpendicular to the interface is quantized, and the electronic states are grouped into electronic subbands. At low temperature, dominant scattering mechanisms in these structures are charged impurity and surfaceroughness scattering. In our model, we include all of the aforementioned dissipative mechanisms.
1994
 Effect of halfspace and interface phonons on the transport properties of AlGaAs/GaAs single heterostructures
[Articolo su rivista]
Bordone, Paolo; P., Lugli
abstract
We present a detailed analysis of the influence of the various phonon modes characteristic of the single heterostructure AlxGa1xAs/GaAs on its electronic transport by using a Monte Carlo simulation. The electronic states of the system are calculated by solving selfconsistently the coupled SchrodingerPoisson equations for the system. LOphonon states are treated within the dielectric continuum model by using two different dielectric functions to describe the two semiconductors, the usual LyddaneSachsTeller expression for GaAs and a generalized two poles expression for AlxGa1xAs. Two sets of optical modes characterize the system, the halfspace LO modes and the interface modes. The scattering rates for the interaction of these modes with the confined electrons are calculated from the Fermi golden rule. A Monte Carlo simulation is then used to study the effect of the electronphonon interaction on the transport properties of a single AlxGa1xAs/GaAs heterostructure in the presence of an electric field applied along the heterointerface. The results of simulations performed at 300 and 77 K compare favorably with available experimental data. Drag and heating effects related to nonequilibrium phonon effects are found and discussed.
1994
 HOTPHONON EFFECT ON NOISE AND DIFFUSION IN GAAS
[Articolo su rivista]
Bordone, Paolo; Reggiani, L; Varani, L; Kuhn, T.
abstract
We analyse the effects of a nonequilibrium phonon population on noise and diffusion phenomena in polar semiconductors. We calculate the current and energy autocorrelation functions and the currentenergy crosscorrelation functions, for both the case with and without hotphonon effects. Owing to the presence of hot phonons, we find an increase of the noise equivalent temperature and of the longitudinal diffusion coefficient at intermediate field strengths below the threshold for negative differential mobility.
1994
 Hotphonon effect on chargecarrier fluctuations in GaAs
[Relazione in Atti di Convegno]
Bordone, Paolo; L., Varani; L., Reggiani; T., Kuhn
abstract
We present a Monte Carlo investigation on the influence of a nonequilibrium phonon population (hot phonons) on second order transport properties in GaAs. We calculate the velocity and energy correlation functions both for the case with and without phonon perturbation. The results show significant modifications in the correlation functions and consequently an increase of the equivalent noise temperature due to the presence of hot phonons.
1994
 PHONON EFFECTS ON ELECTRONIC TRANSPORT IN SINGLE ALXGA1XAS GAAS HETEROJUNCTIONS
[Articolo su rivista]
Bordone, Paolo; Lugli, P; Gulia, M.
abstract
We have studied the transport properties of an AlxGa1xAs/GaAs single heterostructure using a Monte Carlo method, focusing in particular on the effect of the polar interaction between electrons and phonons. A twovalley (GAMMA and L) model for both GaAs and AlxGa1xAs layers has been used, which includes size quantization effects through the numerical selfconsistent solution of the coupled SchrodingerPoisson equations. The optical mode description is given in terms of the dielectric continuum model (DCM); within this model the alloy is described by a twopole dielectric function, which depends on the Al composition. We have then evaluated the scattering probabilities for the confined electrons interacting with halfspace and interface modes. These rates are inserted in our Monte Carlo code to study the electron response to an electric field applied along the heterointerface.
1993
 Influence of hot phonons on electronic noise in GaAs
[Articolo su rivista]
Bordone, Paolo; L., Varani; L., Reggiani; L., Rota; T., Kuhn
abstract
We present a Monte Carlo investigation of the influence of the nonequilibrium phonon population on secondorder transport properties in GaAs. We calculate the velocity and energy autocorrelation functions and the velocity–energy crosscorrelation functions, both for the case with and without phonon perturbation. By comparing the results, we find significant modifications in the correlation functions and consequently in the equivalent noise temperature due to the presence of the nonequilibrium phonons.
1992
 INTERACTION OF ELECTRONS WITH INTERFACE PHONONS IN GAAS/ALAS AND GAAS/ALGAAS HETEROSTRUCTURES
[Articolo su rivista]
P., Lugli; Bordone, Paolo; Molinari, Elisa; H., Rucker; A. M., de Paula; A. C., Maciel; J. F., Ryan; M., Shayegan
abstract
The interaction of electrons with interface phonons is predicted to be of major importance in narrow quantum wells. Timeintegrated Raman measurements of nonequilibrium phonons in GaAs/AlAs structures show strong coupling to AlAs interface modes, in good agreement with theoretical predictions based on a microscopic phonon model. Monte Carlo simulations of timeresolved Raman measurements of interface phonons in GaAs/AlGaAs structures provide further confirmation of this result.
1990
 Effect of phonon confinement in quantum well systems
[Relazione in Atti di Convegno]
P., Lugli; Bordone, Paolo; S., Gualdi; S. M., Goodnick
abstract
We discuss the role of LOphonons confinement in quantum well systems, by comparing two different phonon models that have been proposed in the literature. A critical discussion concerning the use of macroscopic approaches for the description of phonons in two dimensional systems is presented. We use a Monte Carlo simulation which includes nonequilibrium phonon effects as well as carriercarrier scattering to determine the effect of phonon confinent on the relaxation of photoexcited carriers in A1GaAsGaAs quantum wells. Good agreement with available experimental data is found. Even at low excitation densities, intercarrier scattering and phonon reabsorption are important, and need to be taken into account in the interpretation of experimental data.
1989
 Femtosecond phenomena in IIIV semiconductors
[Relazione in Atti di Convegno]
P., Lugli; Bordone, Paolo; S., Gualdi; L., Rota; S. M., Goodnick
abstract
We present a Monte Carlo study of ultrafast phenomena in polar semiconductors, focusing on the relaxation of photoexcited carriers in bulk GaAs, InP, and in AlGaAs/GaAs quantum wells. The importance of intercarrier interaction and carrierphonon scattering are discussed. Very good agreement with experimental results obtained with photoluminescence and Raman spectroscopy is found. A novel method for the treatment of the electronelectron scattering via a moleculardynamics algorithm is also presented and compared with previous approaches.
1989
 Hot phonons in quantum wells system
[Articolo su rivista]
P., Lugli; Bordone, Paolo; S., Gualdi; P., Poli; S. M., Goodnick
abstract
We present an investigation of nonequilibrium LOphonon effects in quantum well systems. Phonon confinement is taken into account by considering esplicitly slab modes in the formulation of Fuchs and Kliever. With respect to the “standard” case, where a tridimensional dispersion is used for the LO phonons, the electronphonon interaction is riduced as result of phonon confinement. We use the Monte Carlo (MC) scheme, which allows the simultaneous study of the coupled electron and phonon dynamics, without requiring any sort of assumption on the respective distribution function. It should be pointed out that the quantization of the phonon wavevector in the direction perpendicular to the interface completely solves the normalization problems of the hotphonon calculation in 2Dsystems. For the case of photoexcitation in AlGaAsGaAs quantum wells we observe a reduction in the cooling rate due to the reabsorption of hot phonon.
1989
 Monte Carlo studies of nonequilibrium phonon effects in polar semiconductors and quantum wells. I. Laser photoexcitation
[Articolo su rivista]
P., Lugli; Bordone, Paolo; L., Reggiani; M., Rieger; P., Kocevar; S. M., Goodnick
abstract
The present paper illustrates a series of theoretical results on nonequilibrium phonon effects based on a novel Monte Carlo algorithm. The details of the numerical procedure are given. No assumptions on the form of the phonon or the electron distributions are required. The main emphasis is given to the study of LOphonon perturbations as a result of the relaxation of photoexcited carriers in polar semiconductors. Bulk GaAs and InP, as well as GaAsAlxGa1xAs heterostructures are analyzed. Good agreement is found with available experimental results from timeresolved luminescence and Raman measurements. The strong phonon emission by the highenergy photoexcited electrons in the first stage of their relaxation (within a few tenths of a picosecond) is found to drive the phonon distribution strongly out of equilibrium. After the excitation, reabsorption of the emitted phonons by the carriers and nonelectronic phonondecay processes bring the distribution back to its equilibrium value.
1989
 Monte Carlo studies of nonequilibrium phonon effects in polar semiconductors and quantum wells. II. NonOhmic transport in ntype gallium arsenide
[Articolo su rivista]
M., Rieger; P., Kocevar; P., Lugli; Bordone, Paolo; L., Reggiani; S. M., Goodnick
abstract
Effects of LOphonon disturbances on the transient and steadystate high–dcfield response of ntype gallium arsenide are studied by implementing the simulation of nonequilibrium phonon distributions into the conventional Monte Carlo algorithms for hotcarrier transport in semiconductors. Strong LOphonon amplification is found for the whole range of fields, carrier densities, and temperatures of interest. At room temperature the phonon disturbances lead to enhancements of up to 20% of the steadystate velocity at low fields and to reductions of up to 10% for fields around and above the maximum of the velocityfield characteristics. However, detailed phasespace restrictions for LOphonon reabsorption prevent a noticeable interference of the phonon buildup with the transient velocity overshoot.
1988
 Transient hotphonon effects on the velocity overshoot of GaAs: a Monte Carlo analysis
[Articolo su rivista]
M., Rieger; P., Kocevar; Bordone, Paolo; P., Lugli; L., Reggiani
abstract
A novel ensemble Monte Carlo algorithm has been developed to simulate nonequilibrium phonon effects in the transient and steadystate highfield conductivity of bulk nGaAs. The interplay of the electronic intervalley transfer with the mutual drag and heating between the carriers and longitudinal optical phonons is demonstrated over a wide range of fields, temperatures and carrier densities.For the moderately high doping levels of practical interest the characteristic times for a strong phonon amplification turn out to be sufficiently long to prevent a substantial interference of phonon disturbances with the onset of valley transfer during overshoot, but modifications of up to 20 percent are found for the steadystate velocity, with a gradual change from an enhancement at low fields to a comparable decrease around the maximum and negative differential part of the velocityfield characteristics.Comparable nonequilibriumphonon effects are found for the case of negligible (i.e. remote) ionizedimpurity scattering as realized in various GaAsbased heterostructures.
1987
 Effect of a perturbed acousticphonon distribution on hotelectron transport: a Monte Carlo analysis
[Articolo su rivista]
Bordone, Paolo; Jacoboni, Carlo; P., Lugli; L., Reggiani; P., Kocevar
abstract
A Monte Carlo simulation code has been developed to study the effect of phonon perturbations in hotelectron transport in semiconductors. The modifications of carrier drift velocity and mean energy induced by the perturbed acousticphonon distribution are studied at low temperatures in pGe. Under appropriate conditions, current saturation is obtained as a result of the steadystate phonon perturbation. The Monte Carlo analysis has been complemented and compared with an analytical approach based on a heated and displaced Maxwellian distribution for the electron gas.
1985
 Monte Carlo analysis of hotphonon effects on nonpolar semiconductors transport properties
[Articolo su rivista]
Bordone, Paolo; Jacoboni, Carlo; P., Lugli; L., Reggiani; P., Kocevar
abstract
An iterative procedure to include phonon disturbance into a Monte Carlo algorithm is presented. Low temperature transport in pGe is considered. Calculations show that carrier drift velocity and mean energy increase as a result of the phonon amplification.