Growth of entanglement entropy under local projective measurementsCoppola M., Tirrito E., Karevski D.,
Nonequilibrium dynamics of many-body quantum systems under the effect of measurement protocols is attracting an increasing amount of attention. It has been recently revealed that measurements may induce an abrupt change in the scaling law of the bipartite entanglement entropy, thus suggesting the existence of different nonequilibrium regimes. However, our understanding of how these regimes appear and whether they survive in the thermodynamic limit is much less established. Here we investigate these questions on a one-dimensional quadratic fermionic model: this allows us to reach system sizes relevant in the thermodynamic sense. We show that local projective measurements induce a qualitative modification of the time growth of the entanglement entropy which changes from linear to logarithmic. However, in the stationary regime, the logarithmic behavior of the entanglement entropy does not survive in the thermodynamic limit and, for any finite value of the measurement rate, we numerically show the existence of a single area-law phase for the entanglement entropy. Finally, exploiting the quasiparticle picture, we further support our results by analyzing the fluctuations of the stationary entanglement entropy and its scaling behavior.
Heat rectification through single and coupled quantum dotsTesser L., Bhandari B., Erdman P.A., Paladino E.,
We study heat rectification through quantum dots in the Coulomb blockade regime using a master equation approach. We consider both cases of two-terminal and four-terminal devices. In the two-terminal configuration, we analyze the case of a single quantum dot with either a doubly-degenerate level or two non-degenerate levels. In the sequential tunneling regime we analyze the behaviour of heat currents and rectification as functions of the position of the energy levels and of the temperature bias. In particular, we derive an upper bound for rectification in the closed-circuit setup with the doubly-degenerate level. We also prove the absence of a bound for the case of two non-degenerate levels and identify the ideal system parameters to achieve nearly perfect rectification. The second part of the paper deals with the effect of second-order cotunneling contributions, including both elastic and inelastic processes. In all cases we find that there exists ranges of values of parameters (such as the levels' position) where rectification is enhanced by cotunneling. In particular, in the doubly-degenerate level case we find that cotunneling corrections can enhance rectification when they reduce the magnitude of the heat currents. For the four-terminal configuration, we analyze the non-local situation of two Coulomb-coupled quantum dots, each connected to two terminals: the temperature bias is applied to the two terminals connected to one quantum dot, while the heat currents of interest are the ones flowing in the other quantum dot. Remarkably, in this situation we find that non-local rectification can be perfect as a consequence of the fact that the heat currents vanish for properly tuned parameters.
H→0 limit of the entanglement entropy
Entangled quantum states share properties that do not have classical analogs; in particular, they show correlations that can violate Bell inequalities. It is, therefore, an interesting question to see what happens to entanglement measures - such as the entanglement entropy for a pure state - taking the semiclassical limit, where the naive expectation is that they may become singular or zero. This conclusion is, however, incorrect. In this paper, we determine the ℏ→0 limit of the bipartite entanglement entropy for a one-dimensional system of N quantum particles in an external potential and we explicitly show that this limit is finite. Moreover, if the particles are fermionic, we show that the ℏ→0 limit of the bipartite entanglement entropy coincides with the Shannon entropy of N bits.
Taking the temperature of a pure quantum stateMitchison M.T., Purkayastha A., Brenes M.,
Temperature is a deceptively simple concept that still raises deep questions at the forefront of quantum physics research. The observation of thermalization in completely isolated quantum systems, such as cold-atom quantum simulators, implies that a temperature can be assigned even to individual, pure quantum states. Here, we propose a scheme to measure the temperature of such pure states through quantum interference. Our proposal involves interferometry of an auxiliary qubit probe, which is prepared in a superposition state and subsequently decoheres due to weak coupling with a closed, thermalized many-body system. Using only a few basic assumptions about chaotic quantum systems, namely, the eigenstate thermalization hypothesis and the emergence of hydrodynamics at long times, we show that the qubit undergoes pure exponential decoherence at a rate that depends on the temperature of its surroundings. We verify our predictions by numerical experiments on a quantum spin chain that thermalizes after absorbing energy from a periodic drive. Our Letter provides a general method to measure the temperature of isolated, strongly interacting systems under minimal assumptions.
Correlation engineering via nonlocal dissipationSeetharam K., Lerose A.,
Controlling the spread of correlations in quantum many-body systems is a key challenge at the heart of quantum science and technology. Correlations are usually destroyed by dissipation arising from coupling between a system and its environment. Here, we show that dissipation can instead be used to engineer a wide variety of spatiotemporal correlation profiles in an easily tunable manner. We describe how dissipation with any translationally invariant spatial profile can be realized in cold atoms trapped in an optical cavity. A uniform external field and the choice of spatial profile can be used to design when and how dissipation creates or destroys correlations. We demonstrate this control by generating entanglement preferentially sensitive to a desired spatial component of a magnetic field. We thus establish nonlocal dissipation as a route toward engineering the far-from-equilibrium dynamics of quantum information, with potential applications in quantum metrology, state preparation, and transport.
Present status and future challenges of non-interferometric tests of collapse modelsCarlesso M., Donadi S., Ferialdi L., Paternostro M., Ulbricht H.,
The superposition principle is the cornerstone of quantum mechanics, leading to a variety of genuinely quantum effects. Whether the principle applies also to macroscopic systems or, instead, there is a progressive breakdown when moving to larger scales is a fundamental and still open question. Spontaneous wavefunction collapse models predict the latter option, thus questioning the universality of quantum mechanics. Technological advances allow to increasingly challenge collapse models and the quantum superposition principle, with a variety of different experiments. Among them, non-interferometric experiments proved to be the most effective in testing these models. We provide an overview of such experiments, including cold atoms, optomechanical systems, X-ray detection, bulk heating and comparisons with cosmological observations. We also discuss avenues for future dedicated experiments, which aim at further testing collapse models and the validity of quantum mechanics.
Energy fluctuation relations and repeated quantum measurementsGherardini S., Buffoni L., Giachetti G.,
In this paper, we discuss the statistical description in non-equilibrium regimes of energy fluctuations originated by the interaction between a quantum system and a measurement apparatus applying a sequence of repeated quantum measurements. To properly quantify the information about energy fluctuations, both the exchanged heat probability density function and the corresponding characteristic function are derived and interpreted. Then, we discuss the conditions allowing for the validity of the fluctuation theorem in Jarzynski form 〈e−βQ〉=1, thus showing that the fluctuation relation is robust against the presence of randomness in the time intervals between measurements. Moreover, also the late-time, asymptotic properties of the heat characteristic function are analyzed, in the thermodynamic limit of many intermediate quantum measurements. In such a limit, the quantum system tends to the maximally mixed state (thus corresponding to a thermal state with infinite temperature) unless the system's Hamiltonian and the intermediate measurement observable share a common invariant subspace. Then, in this context, we also discuss how energy fluctuation relations change when the system operates in the quantum Zeno regime. Finally, the theoretical results are illustrated for the special cases of two- and three-levels quantum systems, now ubiquitous for quantum applications and technologies.
Mimicking Multiorbital Systems with SU(N) Atoms: Hund’s Physics and BeyondRichaud A., Ferraretto M.,
The physics of many interesting correlated materials can be captured by multiorbital Hubbard models, where conduction electrons feature an additional orbital degree of freedom. The multiorbital characteristic is not a mere complication, but it leads to an immensely richer landscape of physical regimes. One of the key features is the interplay between Hubbard repulsion and Hund’s exchange coupling, which has been shown to lead to orbital-selective correlations and to the existence of correlation-resilient metals (usually called Hund’s metals) defying Mott localization. Here, we show that experimentally available platforms of SU(N)-symmetric ultracold atoms can indeed mimic the rich physics disclosed by multiorbital materials, by exploiting the internal degrees of freedom of multicomponent atoms. We discuss in detail the SU(N) version of interaction-resilient Hund’s metal and some other interesting regimes.
Seeding Crystallization in TimeHajdušek M., Solanki P.,
We introduce the concept of seeding of crystallization in time by studying the dynamics of an ensemble of coupled continuous time crystals. We demonstrate that a single subsystem in a broken-symmetry phase acting as a nucleation center may induce time-translation symmetry breaking across the entire ensemble. Seeding is observed for both coherent and dissipative coupling, as well as for a broad range of parameter regimes. In the spirit of mutual synchronization, we investigate the parameter regime where all subsystems are in the broken-symmetry phase. We observe that more broadly detuned time crystals require weaker coupling strength to be synchronized. This is in contrast to basic knowledge from classical as well as quantum synchronization theory. We show that this surprising observation is a direct consequence of the seeding effect.
Finite-temperature quantum discordant criticalityTarabunga P.S., Mendes-Santos T., Illuminati F.,
In quantum statistical mechanics, finite-temperature phase transitions are typically governed by classical field theories. In this context, the role of quantum correlations is unclear: recent contributions have shown how entanglement is typically very short-ranged, and thus uninformative about long-ranged critical correlations. In this work, we show the existence of finite-temperature phase transitions where a broader form of quantum correlation than entanglement, the entropic quantum discord, can display genuine signatures of critical behavior. We consider integrable bosonic field theories in both two- and three-dimensional lattices, and show how the two-mode Gaussian discord decays algebraically with the distance even in cases where the entanglement negativity vanishes beyond nearest-neighbor separations. Systematically approaching the zero-temperature limit allows us to connect discord to entanglement, drawing a generic picture of quantum correlations and critical behavior that naturally describes the transition between entangled and discordant quantum matter.
Optimal quantum annealing: A variational shortcut-to-adiabaticity approachPassarelli G.,
Suppressing unwanted transitions out of the instantaneous ground state is a major challenge in unitary adiabatic quantum computation. A recent approach consists in building counterdiabatic potentials approximated using variational strategies. In this contribution, we extend this variational approach to Lindbladian dynamics, having as a goal the suppression of diabatic transitions between pairs of Jordan blocks in quantum annealing. We show that, surprisingly, unitary counterdiabatic Ansätze are successful for dissipative dynamics as well, allowing for easier experimental implementations compared to Lindbladian Ansätze involving dissipation. Our approach not only guarantees improvements of open-system adiabaticity but also enhances the success probability of quantum annealing.
On the continuum limit of the entanglement Hamiltonian of a sphere for the free massless scalar fieldJaverzat N.,
We study the continuum limit of the entanglement Hamiltonian of a sphere for the massless scalar field in its ground state by employing the lattice model defined through the discretisation of the radial direction. In two and three spatial dimensions and for small values of the total angular momentum, we find numerical results in agreement with the corresponding ones derived from the entanglement Hamiltonian predicted by conformal field theory. When the mass parameter in the lattice model is large enough, the dominant contributions come from the on-site and the nearest-neighbour terms, whose weight functions are straight lines.
Quantum dynamics of few dipolar bosons in a double-well potentialRoy R., Chakrabarti B.,
Abstract: We study the few-body dynamics of dipolar bosons in one-dimensional double-wells. By varying the interaction strength and investigating one-body observables, in the considered few-body systems we study tunneling oscillations, self-trapping, and a regime exhibiting an equilibrating behavior. The corresponding two-body correlation dynamics exhibits a strong interplay between the interatomic correlation due to non-local nature of the repulsion and the inter-well coherence. We also study the link between the correlation dynamics and the occupation of natural orbitals of the one-body density matrix. Graphical abstract: [Figure not available: see fulltext.]
Localization in the Discrete Non-linear Schrödinger Equation and Geometric Properties of the Microcanonical SurfaceArezzo C., Balducci F., Piergallini R.,
It is well known that, if the initial conditions have sufficiently high energy density, the dynamics of the classical Discrete Non-Linear Schrödinger Equation (DNLSE) on a lattice shows a form of breaking of ergodicity, with a finite fraction of the total charge accumulating on a few sites and residing there for times that diverge quickly in the thermodynamic limit. In this paper we show that this kind of localization can be attributed to some geometric properties of the microcanonical potential energy surface, and that it can be associated to a phase transition in the lowest eigenvalue of the Laplacian on said surface. We also show that the approximation of considering the phase space motion on the potential energy surface only, with effective decoupling of the potential and kinetic partition functions, is justified in the large connectivity limit, or fully connected model. In this model we further observe a synchronization transition, with a synchronized phase at low temperatures.
Space-warp coordinate transformation for efficient ionic force calculations in quantum Monte CarloNakano K., Raghav A.,
Ab initio quantum Monte Carlo (QMC) methods are a state-of-The-Art computational approach to obtaining highly accurate many-body wave functions. Although QMC methods are widely used in physics and chemistry to compute ground-state energies, calculation of atomic forces is still under technical/algorithmic development. Very recently, force evaluation has started to become of paramount importance for the generation of machine-learning force-field potentials. Nevertheless, there is no consensus regarding whether an efficient algorithm is available for the QMC force evaluation, namely, one that scales well with the number of electrons and the atomic numbers. In this study, we benchmark the accuracy of all-electron variational Monte Carlo (VMC) and lattice-regularized diffusion Monte Carlo (LRDMC) forces for various mono-and heteronuclear dimers (1 ? Z ? 35, where Z is the atomic number). The VMC and LRDMC forces were calculated with and without the so-called space-warp coordinate transformation (SWCT) and appropriate regularization techniques to remove the infinite variance problem. The LRDMC forces were computed with the Reynolds (RE) and variational-drift (VD) approximations. The potential energy surfaces obtained from the LRDMC energies give equilibrium bond lengths (req) and harmonic frequencies (?) very close to the experimental values for all dimers, improving the corresponding VMC results. The LRDMC forces with the RE approximation improve the VMC forces, implying that it is worth computing the DMC forces beyond VMC despite the higher computational cost. The LRDMC forces with the VD approximations also show improvement, which unfortunately comes at a much higher computational cost in all-electron calculations. We find that the ratio of computational costs between QMC energy and forces scales as Z?2.5 without the SWCT. In contrast, the application of the SWCT makes the ratio independent of Z. As such, the accessible QMC system size is not affected by the evaluation of ionic forces but governed by the same scaling as the total energy one.
Multistage Kondo effect in a multiterminal geometry: A modular quantum interferometerKarki D.B., Pavlov A.I.,
Quantum systems characterized by an interplay between several resonance scattering channels demonstrate very rich physics. To illustrate it we consider a multistage Kondo effect in nanodevices as a paradigmatic model for a multimode resonance scattering. We show that the channel crosstalk results in a destructive interference between the modes. This interplay can be controlled by manipulating the tunneling junctions in the multilevel and multiterminal geometry. We present a full-fledged theory of the multistage Kondo effect at the strong-coupling Fermi-liquid fixed point and discuss the influence of quantum interference effects to the quantum transport observables.
Quantum generalized hydrodynamics of the Tonks-Girardeau gas: Density fluctuations and entanglement entropyRuggiero P.,
We apply the theory of quantum generalized hydrodynamics (QGHD) introduced in (2020 Phys. Rev. Lett. 124 140603) to derive asymptotically exact results for the density fluctuations and the entanglement entropy of a one-dimensional trapped Bose gas in the Tonks-Girardeau (TG) or hard-core limit, after a trap quench from a double well to a single well. On the analytical side, the quadratic nature of the theory of QGHD is complemented with the emerging conformal invariance at the TG point to fix the universal part of those quantities. Moreover, the well-known mapping of hard-core bosons to free fermions, allows to use a generalized form of the Fisher-Hartwig conjecture to fix the non-trivial spacetime dependence of the ultraviolet cutoff in the entanglement entropy. The free nature of the TG gas also allows for more accurate results on the numerical side, where a higher number of particles as compared to the interacting case can be simulated. The agreement between analytical and numerical predictions is extremely good. For the density fluctuations, however, one has to average out large Friedel oscillations present in the numerics to recover such agreement.
Dissipative Floquet Dynamics: from Steady State to Measurement Induced Criticality in Trapped-ion ChainsSierant P., Chiriacò G., Surace F.M., Sharma S., Turkeshi X.,
Quantum systems evolving unitarily and subject to quantum measurements exhibit various types of non-equilibrium phase transitions, arising from the competition between unitary evolution and measurements. Dissipative phase transitions in steady states of time-independent Liouvillians and measurement induced phase transitions at the level of quantum trajectories are two primary examples of such transitions. Investigating a many-body spin system subject to periodic resetting measurements, we argue that many-body dissipative Floquet dynamics provides a natural framework to analyze both types of transitions. We show that a dissipative phase transition between a ferromagnetic ordered phase and a paramagnetic disordered phase emerges for long-range systems as a function of measurement probabilities. A measurement induced transition of the entanglement entropy between volume law scaling and sub-volume law scaling is also present, and is distinct from the ordering transition. The two phases correspond to an error-correcting and a quantum-Zeno regimes, respectively. The ferromagnetic phase is lost for short range interactions, while the volume law phase of the entanglement is enhanced. An analysis of multifractal properties of wave function in Hilbert space provides a common perspective on both types of transitions in the system. Our findings are immediately relevant to trapped ion experiments, for which we detail a blueprint proposal based on currently available platforms.
Real-time evolution in the Hubbard model with infinite repulsionTartaglia E.,
We consider the real-time evolution of the Hubbard model in the limit of infinite coupling. In this limit the Hamiltonian of the system is mapped into a number-conserving quadratic form of spinless fermions, i.e. the tight binding model. The relevant local observables, however, do not transform well under this mapping and take very complicated expressions in terms of the spinless fermions. Here we show that for two classes of interesting observables the quench dynamics from product states in the occupation basis can be determined exactly in terms of correlations in the tight-binding model. In particular, we show that the time evolution of any function of the total density of particles is mapped directly into that of the same function of the density of spinless fermions in the tight-binding model. Moreover, we express the two-point functions of the spin-full fermions at any time after the quench in terms of correlations of the tight binding model. This sum is generically very complicated but we show that it leads to simple explicit expressions for the time evolution of the densities of the two separate species and the correlations between a point at the boundary and one in the bulk when evolving from the so called generalised nested Néel states.
Dissipative cooling induced by pulse perturbationsNava A.,
We investigate the dynamics brought on by an impulse perturbation in two infinite-range quantum Ising models coupled to each other and to a dissipative bath. We show that, if dissipation is faster the higher the excitation energy, the pulse perturbation cools down the low-energy sector of the system, at the expense of the high-energy one, eventually stabilising a transient symmetry-broken state at temperatures higher than the equilibrium critical one. Such non-thermal quasi-steady state may survive for quite a long time after the pulse, if the latter is properly tailored.