arXiv subjects

Rosario Fazio

Publications and source records attributed to Rosario Fazio.

At least 127 records · Page 7Linked to original sources

arXiv2017

Dissipation in adiabatic quantum computers: Lessons from an exactly solvable model

We introduce and study the adiabatic dynamics of free-fermion models subject to a local Lindblad bath and in the presence of a time-dependent Hamiltonian. The merit of these models is that they can be solved exactly, and will help us to study the interplay between non-adiabatic transitions and dissipation in many-body quantum systems. After the adiabatic evolution, we evaluate the excess energy (average value of the Hamiltonian) as a measure of the deviation from reaching the target final ground state. We compute the excess energy in a variety of different situations, where the nature of the bath and the Hamiltonian is modified. We find a robust evidence of the fact that an optimal working time for the quantum annealing protocol emerges as a result of the competition between the non-adiabatic effects and the dissipative processes. We compare these results with matrix-product-operator simulations of an Ising system and show that the phenomenology we found applies also for this more realistic case.

quant-ph↗

arXiv2017

Linked cluster expansions for open quantum systems on a lattice

We propose a generalization of the linked-cluster expansions to study driven-dissipative quantum lattice models, directly accessing the thermodynamic limit of the system. Our method leads to the evaluation of the desired extensive property onto small connected clusters of a given size and topology. We first test this approach on the isotropic spin-1/2 Hamiltonian in two dimensions, where each spin is coupled to an independent environment that induces incoherent spin flips. Then we apply it to the study of an anisotropic model displaying a dissipative phase transition from a magnetically ordered to a disordered phase. By means of a Padé analysis on the series expansions for the average magnetization, we provide a viable route to locate the phase transition and to extrapolate the critical exponent for the magnetic susceptibility.

cond-mat.stat-mech↗

arXiv2017

Density-of-states of many-body quantum systems from tensor networks

We present a technique to compute the microcanonical thermodynamical properties of a manybody quantum system using tensor networks. The Density Of States (DOS), and more general spectral properties, are evaluated by means of a Hubbard-Stratonovich transformation performed on top of a real-time evolution, which is carried out via numerical methods based on tensor networks. As a consequence, the free energy and thermal averages can be also calculated. We test this approach on the one-dimensional Ising and Fermi-Hubbard models. Using matrix product states, we show that the thermodynamical quantities as a function of temperature are in very good agreement with the exact results. This approach can be extended to higher-dimensional system by properly employing other types of tensor networks.

quant-ph↗

arXiv2017

Phase diagram of incoherently driven strongly correlated photonic lattices

We explore theoretically the nonequilibrium photonic phases of an array of coupled cavities in presence of incoherent driving and dissipation. In particular, we consider a Hubbard model system where each site is a Kerr nonlinear resonator coupled to a two-level emitter, which is pumped incoherently. Within a Gutzwiller mean-field approach, we determine the steady-state phase diagram of such a system. We find that, at a critical value of the inter-cavity photon hopping rate, a second-order nonequilibrium phase transition associated with the spontaneous breaking of the $U(1)$ symmetry occurs. The transition from an incompressible Mott-like photon fluid to a coherent delocalized phase is driven by commensurability effects and not by the competition between photon hopping and optical nonlinearity. The essence of the mean-field predictions is corroborated by finite-size simulations obtained with matrix product operators and corner-space renormalization methods.

cond-mat.other↗

arXiv2017

Stabilizing strongly correlated photon fluids with non-Markovian reservoirs

We introduce a novel frequency-dependent incoherent pump scheme with a square-shaped spectrum as a way to study strongly correlated photons in arrays of coupled nonlinear resonators. This scheme can be implemented via a reservoir of population-inverted two-level emitters with a broad distribution of transition frequencies. Our proposal is predicted to stabilize a non-equilibrium steady state sharing important features with a zero-temperature equilibrium state with a tunable chemical potential. We confirm the efficiency of our proposal for the Bose-Hubbard model by computing numerically the steady state for finite system sizes: first, we predict the occurrence of a sequence of incompressible Mott-Insulator-like states with arbitrary integer densities presenting strong robustness against tunneling and losses. Secondly, for stronger tunneling amplitudes or non-integer densities, the system enters a coherent regime analogous to the superfluid state. In addition to an overall agreement with the zero-temperature equilibrium state, exotic non-equilibrium processes leading to a finite entropy generation are pointed out in specific regions of parameter space. The equilibrium ground state is shown to be recovered by adding frequency-dependent losses. The promise of this improved scheme in view of quantum simulation of the zero temperature many-body physics is highlighted.

quant-ph↗

arXiv2017

Direct comparison of quantum and simulated annealing on a fully-connected Ising ferromagnet

We compare the performance of quantum annealing (QA, through Schrödinger dynamics) and simulated annealing (SA, through a classical master equation) on the $p$-spin infinite range ferromagnetic Ising model, by slowly driving the system across its equilibrium, quantum or classical, phase transition. When the phase transition is second-order ($p=2$, the familiar two-spin Ising interaction) SA shows a remarkable exponential speed-up over QA. For a first-order phase transition ($p \ge 3$, i.e., with multi-spin Ising interactions), in contrast, the classical annealing dynamics appears to remain stuck in the disordered phase, while we have clear evidence that QA shows a residual energy which decreases towards $0$ when the total annealing time $τ$ increases, albeit in a rather slow (logarithmic) fashion. This is one of the rare examples where a limited quantum speedup, a speedup by QA over SA, has been shown to exist by direct solutions of the Schrödinger and master equations in combination with a non-equilibrium Landau-Zener analysis. We also analyse the imaginary-time QA dynamics of the model, finding a $1/τ^2$ behaviour for all finite values of $p$, as predicted by the adiabatic theorem of quantum mechanics. The Grover-search limit $p({\rm odd})=\infty$ is also discussed.

quant-ph↗

arXiv2017

Floquet time crystal in the Lipkin-Meshkov-Glick model

In this work we discuss the existence of time-translation symmetry breaking in a kicked infinite-range-interacting clean spin system described by the Lipkin-Meshkov-Glick model. This Floquet time crystal is robust under perturbations of the kicking protocol, its existence being intimately linked to the underlying $\mathbb{Z}_2$ symmetry breaking of the time-independent model. We show that the model being infinite-range and having an extensive amount of symmetry breaking eigenstates is essential for having the time-crystal behaviour. In particular we discuss the properties of the Floquet spectrum, and show the existence of doublets of Floquet states which are respectively even and odd superposition of symmetry broken states and have quasi-energies differing of half the driving frequencies, a key essence of Floquet time crystals. Remarkably, the stability of the time-crystal phase can be directly analysed in the limit of infinite size, discussing the properties of the corresponding classical phase space. Through a detailed analysis of the robustness of the time crystal to various perturbations we are able to map the corresponding phase diagram. We finally discuss the possibility of an experimental implementation by means of trapped ions.

cond-mat.stat-mech↗

arXiv2017

Thermoelectric properties of an interacting quantum dot-based heat engine

We study the thermoelectric properties and heat-to-work conversion performance of an interacting, multi-level quantum dot (QD) weakly coupled to electronic reservoirs. We focus on the sequential tunneling regime. The dynamics of the charge in the QD is studied by means of master equations for the probabilities of occupation. From here we compute the charge and heat currents in the linear response regime. Assuming a generic multi-terminal setup, and for low temperatures (quantum limit), we obtain analytical expressions for the transport coefficients which account for the interplay between interactions (charging energy) and level quantization. In the case of systems with two and three terminals we derive formulas for the power factor Q and the figure of merit ZT for a QD-based heat engine, identifying optimal working conditions which maximize output power and efficiency of heat-to-work conversion. Beyond the linear response we concentrate on the two-terminal setup. We first study the thermoelectric non-linear coefficients assessing the consequences of large temperature and voltage biases, focusing on the breakdown of the Onsager reciprocal relation between thermopower and Peltier coefficient. We then investigate the conditions which optimize the performance of a heat engine, finding that in the quantum limit output power and efficiency at maximum power can almost be simultaneously maximized by choosing appropriate values of electrochemical potential and bias voltage. At last we study how energy level degeneracy can increase the output power.

cond-mat.mes-hall↗

arXiv2017

One-dimensional Repulsive Fermi Gas in a Tunable Periodic Potential

By using unbiased continuos-space quantum Monte Carlo simulations, we investigate the ground state properties of a one-dimensional repulsive Fermi gas subjected to a commensurate periodic optical lattice (OL) of arbitrary intensity. The equation of state and the magnetic structure factor are determined as a function of the interaction strength and of the OL intensity. In the weak OL limit, Yang's theory for the energy of a homogeneous Fermi gas is recovered. In the opposite limit (deep OL), we analyze the convergence to the Lieb-Wu theory for the Hubbard model, comparing two approaches to map the continuous-space to the discrete-lattice model: the first is based on (noninteracting) Wannier functions, the second effectively takes into account strong-interaction effects within a parabolic approximation of the OL wells. We find that strong antiferromagnetic correlations emerge in deep OLs, and also in very shallow OLs if the interaction strength approaches the Tonks-Girardeau limit. In deep OLs we find quantitative agreement with density matrix renormalization group calculations for the Hubbard model. The spatial decay of the antiferromagnetic correlations is consistent with quasi long-range order even in shallow OLs, in agreement with previous theories for the half-filled Hubbard model.

cond-mat.quant-gas↗

arXiv2017

Laughlin-like states in bosonic and fermionic atomic synthetic ladders

The combination of interactions and static gauge fields plays a pivotal role in our understanding of strongly-correlated quantum matter. Cold atomic gases endowed with a synthetic dimension are emerging as an ideal platform to experimentally address this interplay in quasi-one-dimensional systems. A fundamental question is whether these setups can give access to pristine two-dimensional phenomena, such as the fractional quantum Hall effect, and how. We show that unambiguous signatures of bosonic and fermionic Laughlin-like states can be observed and characterized in synthetic ladders. We theoretically diagnose these Laughlin-like states focusing on the chiral current flowing in the ladder, on the central charge of the low-energy theory, and on the properties of the entanglement entropy. Remarkably, Laughlin-like states are separated from conventional liquids by Lifschitz-type transitions, characterized by sharp discontinuities in the current profiles, which we address using extensive simulations based on matrix-product states. Our work provides a qualitative and quantitative guideline towards the observability and understanding of strongly-correlated states of matter in synthetic ladders. In particular, we unveil how state-of-the-art experimental settings constitute an ideal starting point to progressively tackle two-dimensional strongly interacting systems from a ladder viewpoint, opening a new perspective for the observation of non-Abelian states of matter.

cond-mat.quant-gas↗

arXiv2017

Feedback controlled heat transport in quantum devices: Theory and solid state experimental proposal

A theory of feedback controlled heat transport in quantum systems is presented. It is based on modelling heat engines as driven multipartite systems subject to projective quantum measurements and measurement-conditioned unitary evolutions. The theory unifies various results presented in the previous literature. Feedback control breaks time reversal invariance. This in turn results in the fluctuation relation not being obeyed. Its restoration occurs by an appropriate accounting of the information gain and information use via measurements and feedback. We further illustrate an experimental proposal for the realisation of a Maxwell demon using superconducting circuits and single photon on-chip calorimetry. A two level qubit acts as a trapdoor which, conditioned on its state is coupled to either a hot resistor or a cold one. The feedback mechanism alters the temperatures felt by the qubit and can result in an effective inversion of temperature gradient, where heat flows from cold to hot thanks to information gain and use

cond-mat.mes-hall↗

arXiv2017

Multipartite entanglement after a quantum quench

We study the multipartite entanglement of a quantum many-body system undergoing a quantum quench. We quantify multipartite entanglement through the quantum Fisher information (QFI) density and we are able to express it after a quench in terms of a generalized response function. For pure state initial conditions and in the thermodynamic limit, we can express the QFI as the fluctuations of an observable computed in the so-called diagonal ensemble. We apply the formalism to the dynamics of a quantum Ising chain after a quench in the transverse field. In this model the asymptotic state is, in almost all cases, more than two-partite entangled. Moreover, starting from the ferromagnetic phase, we find a divergence of multipartite entanglement for small quenches closely connected to a corresponding divergence of the correlation length.

quant-ph↗

arXiv2017

Critical dynamical properties of a first-order dissipative phase transition

We theoretically investigate the critical properties of a single driven-dissipative nonlinear photon mode. In a well-defined thermodynamical limit of large excitation numbers, the exact quantum solution describes a first-order phase transition in the regime where semiclassical theory predicts optical bistability. We study the behavior of the complex spectral gap associated with the Liouvillian superoperator of the corresponding master equation. We show that in this limit the Liouvillian gap vanishes exponentially and that the bimodality of the photon Wigner function disappears. The connection between the considered thermodynamical limit of large photon numbers for the single-mode cavity and the thermodynamical limit of many cavities for a driven-dissipative Bose-Hubbard system is discussed.

quant-ph↗

arXiv2017

Signatures of many-body localisation in the dynamics of two-sites entanglement

We are able to detect clear signatures of dephasing -- a distinct trait of Many-Body Localisation (MBL) -- via the dynamics of two-sites entanglement, quantified through the concurrence. Using the protocol implemented in [Science {\bf 349}, 842 (2015)] we show that -- in the MBL phase -- the average two-site entanglement decays in time as a power law, while in the Anderson localised phase it tends to a plateau. The exponent of the power law is not universal and shows a clear dependence on the strength of the interaction. This behaviour is also qualitatively different in the ergodic phase where the two-site entanglement decays exponentially. All the results are obtained by means of time-dependent density matrix renormalisation group simulations; they are corroborated by analytical calculations on an effective model. Two-site entanglement has been already measured in cold atoms: Our analysis paves the way for the first direct experimental test of many-body dephasing in the MBL phase.

quant-ph↗

arXiv2016

Cluster mean-field approach to the steady-state phase diagram of dissipative spin systems

We show that short-range correlations have a dramatic impact on the steady-state phase diagram of quantum driven-dissipative systems. This effect, never observed in equilibrium, follows from the fact that ordering in the steady state is of dynamical origin, and is established only at very long times, whereas in thermodynamic equilibrium it arises from the properties of the (free) energy. To this end, by combining the cluster methods extensively used in equilibrium phase transitions to quantum trajectories and tensor-network techniques, we extend them to nonequilibrium phase transitions in dissipative many-body systems. We analyze in detail a model of spin-1=2 on a lattice interacting through an XYZ Hamiltonian, each of them coupled to an independent environment that induces incoherent spin flips. In the steady-state phase diagram derived from our cluster approach, the location of the phase boundaries and even its topology radically change, introducing reentrance of the paramagnetic phase as compared to the single-site mean field where correlations are neglected. Furthermore, a stability analysis of the cluster mean field indicates a susceptibility towards a possible incommensurate ordering, not present if short-range correlations are ignored.

cond-mat.stat-mech↗

arXiv2016

Topological fractional pumping with alkaline-earth(-like) ultracold atoms

Alkaline-earth(-like) ultracold atoms, trapped in optical lattices and in the presence of an external gauge field, can stabilise Mott insulating phases characterised by density and magnetic order. We show that this property can be used to realise a topological fractional pump. Our analysis is based on a many-body adiabatic expansion and on time-dependent matrix-product-states numerical simulations. We characterise the pumping protocol by including both finite-size and non-adiabatic corrections. For a specific form of atom-atom interaction, we present an exactly-solvable model of a fractional pump. Finally, the numerical simulations allow us to thoroughly study a realistic setup amenable of an experimental realisation.

cond-mat.quant-gas↗

arXiv2016

Entanglement entropy in a periodically driven Ising chain

In this work we study the entanglement entropy of a uniform quantum Ising chain in transverse field undergoing a periodic driving of period $τ$ . By means of Floquet theory we show that, for any subchain, the entanglement entropy tends asymptotically to a value $τ$ - periodic in time. We provide a semi-analytical formula for the leading term of this asymptotic regime: It is constant in time and obeys a volume law. The entropy in the asymptotic regime is always smaller than the thermal one: because of integrability the system locally relaxes to a Generalized Gibbs Ensemble (GGE) density matrix. The leading term of the asymptotic entanglement entropy is completely determined by this GGE density matrix. Remarkably, the asymptotic entropy shows marked features in correspondence to some non-equilibrium quantum phase transitions undergone by a Floquet state analog of the ground state.

quant-ph↗

arXiv2016

Destruction of string order after a quantum quench

We investigate the evolution of string order in a spin-1 chain following a quantum quench. After initializing the chain in the Affleck-Kennedy-Lieb-Tasaki state, we analyze in detail how string order evolves as a function of time at different length scales. The Hamiltonian after the quench is chosen either to preserve or to suddenly break the symmetry which ensures the presence of string order. Depending on which of these two situations arises, string order is either preserved or lost even at infinitesimal times in the thermodynamic limit. The fact that non-local order may be abruptly destroyed, what we call string-order melting, makes it qualitatively different from typical order parameters in the manner of Landau. This situation is thoroughly characterized by means of numerical simulations based on matrix product states algorithms and analytical studies based on a short-time expansion for several simplified models.

cond-mat.stat-mech↗