arXiv subjects

Andrea Beggi

Publications and source records attributed to Andrea Beggi.

6 recordsLinked to original sources

arXiv2018

Back and forth from Fock space to Hilbert space: a guide for commuters

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 the 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 advices for those students and researchers in the need to commute back and forth from one description to the other. The two-particle case is discussed in some details and few guidelines for numerical implementations are given.

quant-ph↗

arXiv2018

Dynamics and Hall-edge-state mixing of localized electrons in a two-channel Mach-Zehnder interferometer

We present a numerical study of a multichannel electronic Mach-Zehnder interferometer, based on magnetically-driven non-interacting edge states. The electron path is defined by a full-scale potential landscape on the two-dimensional electron gas at filling factor two, assuming initially only the first Landau level as filled. We tailor the two beam splitters with 50% interchannel mixing and measure Aharonov-Bohm oscillations in the transmission probability of the second channel. We perform time-dependent simulations by solving the electron Schroedinger equation through a parallel implementation of the split-step Fourier method and we describe the charge-carrier 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 propose possible strategies to optimize gate performances.

cond-mat.mes-hall↗

arXiv2017

Probing the sign of on-site Hubbard interaction by two-particle quantum walks

We consider two identical bosons propagating on a one-dimensional lattice and address the prob- lem of discriminating whether their mutual on-site interaction is attractive or repulsive. We suggest a probing scheme based on the properties of the corresponding two-particle quantum walks, and show that the sign of the interaction introduces specific and detectable features in the dynamics of quantum correlations, thus permitting to discriminate between the two cases. We also discuss how these features are connected to the band-structure of the Hubbard Hamiltonian, and prove that discrimination may be obtained only when the two walkers are initially prepared in a superposition of localized states.

quant-ph↗

arXiv2016

Quantum correlations of identical particles subject to classical environmental noise

In this work we propose a measure for the quantum discord of indistinguishable particles, based on the definition of entanglement of particles given in [H. M. Wiseman et al., Phis. Rev. Lett 91, 097902 (2003)]. 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 on-site interaction between particles have an important protective effect on correlations against the decoherence of the system.

quant-ph↗

arXiv2015

Time-dependent simulation and analytical modelling of electronic Mach-Zehnder interferometry with edge-states wave packets

We compute the exact single-particle time-resolved dynamics of electronic Mach-Zehnder interferometers based on Landau edge-states 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 time-dependent Schroedinger 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 reproduces the results of Y.Ji et al.[Nature 422, 415 (2003)]. 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 energy-dependent 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.

cond-mat.mes-hall↗

arXiv2014

Analytical expression of Genuine Tripartite Quantum Discord for Symmetrical X-states

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 three-qubit systems characterized by a subclass of symmetrical X-states. 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.

quant-ph↗