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LUCA RAZZOLI
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Pubblicazioni
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 Continuous-Time Quantum Walks on Graphs
[Articolo su rivista]
Razzoli, Luca; Paris, Matteo G. A.; Bordone, Paolo
abstract
Continuous-time 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 light-harvesting 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 environment-assisted 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.
2020
- Continuous-time 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 continuous-time 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 next-nearest-neighbor 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 perturbation-dependent 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
- Continuous-time 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 continuous-time quantum walk (CTQW) on planar two-dimensional (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 well-known ballistic behavior, whereas on the honeycomb lattice graph we obtain a sub-ballistic 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 non-Bravais. 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 pseudo-oscillations, a reminiscence of the harmonic oscillator behind theHamiltonian in the continuum, whose energy levels are the well-known Landau levels.
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 two-dimensional 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
non-negligible 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 coarse-grained position measurement, showing that it may be employed to realize
nearly optimal estimation strategies.
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 two-particle case is discussed in some detail, and
a few guidelines for numerical implementations are given.
2018
- Probing the sign of the Hubbard interaction by two-particle 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 one-dimensional lattice, and suggest a probing scheme exploiting the dynamical properties of the corresponding two-particle 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.