Dissipative time crystals with long-range Lindbladians

Passarelli G., Lucignano P., Dissipative time crystals can appear in spin systems, when the Z2 symmetry of the Hamiltonian is broken by the environment, and the square of total spin operator S2 is conserved. In this paper, we relax the latter condition and show that time-translation-symmetry-breaking collective oscillations persist, in the thermodynamic limit, even in the absence of spin symmetry. We engineer an ad hoc Lindbladian using power-law-decaying spin operators and show that time-translation-symmetry breaking appears when the decay exponent obeys 0<η≤1. This model shows a surprisingly rich phase diagram, including the time-crystal phase as well as first-order, second-order, and continuous transitions of the fixed points. We study the phase diagram and the magnetization dynamics in the mean-field approximation. We prove that this approximation is quantitatively accurate, when 0<η<1 and the thermodynamic limit is taken, because the system does not develop sizable quantum fluctuations, if the Gaussian approximation is considered.

Deep-learning density functionals for gradient descent optimization

Costa E., Scriva G., Machine-learned regression models represent a promising tool to implement accurate and computationally affordable energy-density functionals to solve quantum many-body problems via density functional theory. However, while they can easily be trained to accurately map ground-state density profiles to the corresponding energies, their functional derivatives often turn out to be too noisy, leading to instabilities in self-consistent iterations and in gradient-based searches of the ground-state density profile. We investigate how these instabilities occur when standard deep neural networks are adopted as regression models, and we show how to avoid them by using an ad hoc convolutional architecture featuring an interchannel averaging layer. The main testbed we consider is a realistic model for noninteracting atoms in optical speckle disorder. With the interchannel average, accurate and systematically improvable ground-state energies and density profiles are obtained via gradient-descent optimization, without instabilities nor violations of the variational principle.

Nonlinear dynamics of the dissipative anisotropic two-photon Dicke model

Li J., We study the semiclassical limit of the anisotropic two-photon Dicke model with a dissipative bosonic field and describe its rich nonlinear dynamics. Besides normal and 'superradiant'-like phases, the presence of localized fixed points reflects the spectral collapse of the closed-system Hamiltonian. Through Hopf bifurcations of superradiant and normal fixed points, limit cycles are formed in certain regions of parameters. We also identify a pole-flip transition induced by anisotropy and a region of chaotic dynamics, which appears from a cascade of period-doubling bifurcations. In the chaotic region, collision and fragmentation of symmetric attractors take place. Throughout the phase diagram we find several examples of phase coexistence, leading to the segmentation of phase space into distinct basins of attraction.

Weak ergodicity breaking in Josephson-junction arrays

Russomanno A., Fava M., We study the quantum dynamics of Josephson-junction arrays. We find isolated groups of low-entanglement eigenstates that persist even when the Josephson interaction is strong enough to destroy the overall organization of the spectrum in multiplets, and a perturbative description is no longer possible. These eigenstates lie in the inner part of the spectrum, far from the spectral edge, and provide a weak ergodicity breaking, reminiscent of the quantum scars. Due to the presence of these eigenstates, initializing with a charge-density-wave state, the system does not thermalize and the charge-density-wave order persists for long times. Considering global ergodicity probes, we find that the system tends toward more ergodicity for increasing system size: The parameter range where the bulk of the eigenstates look nonergodic shrinks for increasing system size. We study two geometries, a one-dimensional chain and a two-leg ladder. In the latter case, adding a magnetic flux makes the system more ergodic.

Collective effects on the performance and stability of quantum heat engines

Souza L.D.S., Manzano G., Recent predictions for quantum-mechanical enhancements in the operation of small heat engines have raised renewed interest in their study both from a fundamental perspective and in view of applications. One essential question is whether collective effects may help to carry enhancements over larger scales, when increasing the number of systems composing the working substance of the engine. Such enhancements may consider not only power and efficiency, that is, its performance, but, additionally, its constancy, that is, the stability of the engine with respect to unavoidable environmental fluctuations. We explore this issue by introducing a many-body quantum heat engine model composed by spin pairs working in continuous operation. We study how power, efficiency, and constancy scale with the number of spins composing the engine and introduce a well-defined macroscopic limit where analytical expressions are obtained. Our results predict power enhancements, in both finite-size and macroscopic cases, for a broad range of system parameters and temperatures, without compromising the engine efficiency, accompanied by coherence-enhanced constancy for finite sizes. We discuss these quantities in connection to thermodynamic uncertainty relations.

Entanglement transitions from stochastic resetting of non-Hermitian quasiparticles

Turkeshi X., Dalmonte M., We put forward a phenomenological theory for entanglement dynamics in monitored quantum many-body systems with well-defined quasiparticles. Within this theory entanglement is carried by ballistically propagating non-Hermitian quasiparticles which are stochastically reset by the measurement protocol with a rate given by their finite inverse lifetime. We write down a renewal equation for the statistics of the entanglement entropy and show that, depending on the spectrum of quasiparticle decay rates, different entanglement scalings can arise and even sharp entanglement phase transitions. When applied to a quantum Ising chain where the transverse magnetization is measured by quantum jumps, our theory predicts a critical phase with logarithmic scaling of the entanglement, an area-law phase and a continuous phase transition between them, with an effective central charge vanishing as a square root at the transition point. We compare these predictions with exact numerical calculations on the same model and find an excellent agreement.

Hybrid ferromagnetic transmon qubit: Circuit design, feasibility, and detection protocols for magnetic fluctuations

Ahmad H.G., Brosco V., Miano A., Di Palma L., Arzeo M., Montemurro D., Lucignano P., Pepe G.P., Tafuri F., We propose to exploit currently available tunnel ferromagnetic Josephson junctions to realize a hybrid superconducting qubit. We show that the characteristic hysteretic behavior of the ferromagnetic barrier provides an alternative and intrinsically digital tuning of the qubit frequency by means of magnetic field pulses. To illustrate functionalities and limitation of the device, we discuss the coupling to a readout resonator and the effect of magnetic fluctuations. The possibility to use the qubit as a noise detector and its relevance to investigate the subtle interplay of magnetism and superconductivity is envisaged.

Dynamical scaling of correlations generated by short- and long-range dissipation

Seetharam K., Lerose A., We study the spatiotemporal spreading of correlations in an ensemble of spins due to dissipation characterized by short- and long-range spatial profiles. Such emission channels can be synthesized with tunable spatial profiles in lossy cavity QED experiments using a magnetic field gradient and a Raman drive with multiple sidebands. We consider systems initially in an uncorrelated state, and find that correlations widen and contract in a novel pattern intimately related to both the dissipative nature of the dynamical channel and its spatial profile. Additionally, we make a methodological contribution by generalizing nonequilibrium spin-wave theory to the case of dissipative systems and derive equations of motion for any translationally invariant spin chain whose dynamics can be described by a combination of Hamiltonian interactions and dissipative Lindblad channels. Our work aims at extending the study of correlation dynamics to purely dissipative quantum simulators and compare them with the established paradigm of correlations spreading in Hamiltonian systems.

Measurement-induced criticality in extended and long-range unitary circuits

Sharma S., Turkeshi X., We explore the dynamical phases of unitary Clifford circuits with variable-range interactions, coupled to a monitoring environment. We investigate two classes of models, distinguished by the action of the unitary gates, which either are organized in clusters of finite-range two-body gates, or are pair-wise interactions randomly distributed throughout the system with a power-law distribution. We find the range of the interactions plays a key role in characterizing both phases and their measurement-induced transitions. For the cluster unitary gates we find a transition between a phase with volume-law scaling of the entanglement entropy and a phase with area-law entanglement entropy. Our results indicate that the universality class of the phase transition is compatible to that of short range hybrid Clifford circuits. Oppositely, in the case of power-law distributed gates, we find the universality class of the phase transition changes continuously with the parameter controlling the range of interactions. In particular, for intermediate values of the control parameter, we find a non-conformal critical line which separates a phase with volume-law scaling of the entanglement entropy from one with sub-extensive scaling. Within this region, we find the entanglement entropy and the logarithmic negativity present a cross-over from a phase with algebraic growth of entanglement with system size, and an area-law phase.

Heat rectification through single and coupled quantum dots

Tesser 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.

Correlation engineering via nonlocal dissipation

Seetharam 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.

Seeding Crystallization in Time

Hajdušek 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.

Optimal quantum annealing: A variational shortcut-to-adiabaticity approach

Passarelli 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.

Dissipative Floquet Dynamics: from Steady State to Measurement Induced Criticality in Trapped-ion Chains

Sierant P., Chiriacò G., Surace F.M., Sharma S., Turkeshi X., Dalmonte M., 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.

Determination of the critical exponents in dissipative phase transitions: Coherent anomaly approach

Jin J., He W.B., Iemini F., Ferreira D., Wang Y.D., Chesi S., We propose a generalization of the coherent anomaly method to extract the critical exponents of a phase transition occurring in the steady-state of an open quantum many-body system. The method, originally developed by Suzuki [J. Phys. Soc. Jpn. 55, 4205 (1986)JUPSAU0031-901510.1143/JPSJ.55.4205] for equilibrium systems, is based on the scaling properties of the singularity in the response functions determined through cluster mean-field calculations. We apply this method to the dissipative transverse-field Ising model and the dissipative XYZ model in two dimensions obtaining convergent results already with small clusters.

Fragility of classical Hamiltonian period doubling to quantum fluctuations

Khasseh R., Russomanno A., We add quantum fluctuations to a classical period-doubling Hamiltonian time crystal, replacing the N classical interacting angular momenta with quantum spins of size l. The full permutation symmetry of the Hamiltonian allows a mapping to a bosonic model and the application of exact diagonalization for a quite large system size. In the thermodynamic limit N→∞ the model is described by a system of Gross-Pitaevskii equations whose classical-chaos properties closely mirror the finite-N quantum chaos. For N→∞, and l finite, Rabi oscillations mark the absence of persistent period doubling, which is recovered for l→∞ with Rabi-oscillation frequency tending exponentially to 0. For the chosen initial conditions, we can represent this model in terms of Pauli matrices and apply the discrete truncated Wigner approximation. For finite l this approximation reproduces no Rabi oscillations but correctly predicts the absence of period doubling. Our results show the instability of time-Translation symmetry breaking in this classical system even to the smallest quantum fluctuations, because of tunneling effects.

Intrinsic Dimension of Path Integrals: Data-Mining Quantum Criticality and Emergent Simplicity

Mendes-Santos T., Angelone A., Rodriguez A., Quantum many-body systems are characterized by patterns of correlations defining highly nontrivial manifolds when interpreted as data structures. Physical properties of phases and phase transitions are typically retrieved via correlation functions, that are related to observable response functions. Recent experiments have demonstrated capabilities to fully characterize quantum many-body systems via wave-function snapshots, opening new possibilities to analyze quantum phenomena. Here, we introduce a method to data mine the correlation structure of quantum partition functions via their path integral (or equivalently, stochastic series expansion) manifold. We characterize path-integral manifolds generated via state-of-the-art quantum Monte Carlo methods utilizing the intrinsic dimension (ID) and the variance of distances between nearest-neighbor (NN) configurations: the former is related to data-set complexity, while the latter is able to diagnose connectivity features of points in configuration space. We show how these properties feature universal patterns in the vicinity of quantum criticality, that reveal how data structures simplify systematically at quantum phase transitions. This is further reflected by the fact that both ID and variance of NN distances exhibit universal scaling behavior in the vicinity of second-order and Berezinskii-Kosterlitz-Thouless critical points. Finally, we show how non-Abelian symmetries dramatically influence quantum data sets, due to the nature of (noncommuting) conserved charges in the quantum case. Complementary to neural-network representations, our approach represents a first elementary step towards a systematic characterization of path-integral manifolds before any dimensional reduction is taken, that is informative about universal behavior and complexity, and can find immediate application to both experiments and Monte Carlo simulations.

Dynamical Mean-Field Theory for Markovian Open Quantum Many-Body Systems

Scarlatella O., Clerk A.A., A number of experimental platforms relevant for quantum simulations, ranging from arrays of superconducting circuits hosting correlated states of light to ultracold atoms in optical lattices in the presence of controlled dissipative processes. Their theoretical understanding is hampered by the exponential scaling of their Hilbert space and by their intrinsic nonequilibrium nature, limiting the applicability of many traditional approaches. In this work, we extend the nonequilibrium bosonic dynamical mean-field theory (DMFT) to Markovian open quantum systems. Within DMFT, a Lindblad master equation describing a lattice of dissipative bosonic particles is mapped onto an impurity problem describing a single site embedded in its Markovian environment and coupled to a self-consistent field and to a non-Markovian bath, where the latter accounts for fluctuations beyond Gutzwiller mean-field theory due to the finite lattice connectivity. We develop a nonperturbative approach to solve this bosonic impurity problem, which dresses the impurity, featuring Markovian dissipative channels, with the non-Markovian bath, in a self-consistent scheme based on a resummation of noncrossing diagrams. As a first application of our approach, we address the steady state of a driven-dissipative Bose-Hubbard model with two-body losses and incoherent pump. We show that DMFT captures hopping-induced dissipative processes, completely missed in Gutzwiller mean-field theory, which crucially determine the properties of the normal phase, including the redistribution of steady-state populations, the suppression of local gain, and the emergence of a stationary quantum-Zeno regime. We argue that these processes compete with coherent hopping to determine the phase transition toward a nonequilibrium superfluid, leading to a strong renormalization of the phase boundary at finite connectivity. We show that this transition occurs as a finite-frequency instability, leading to an oscillating-in-time order parameter, that we connect with a quantum many-body synchronization transition of an array of quantum van der Pol oscillators.

Quantum phase transition of many interacting spins coupled to a bosonic bath: Static and dynamical properties

De Filippis G., De Candia A., Mishchenko A.S., Cangemi L.M., Nocera A., Mishchenko P.A., Sassetti M., By using worldline and diagrammatic quantum Monte Carlo techniques, matrix product state, and a variational approach à la Feynman, we investigate the equilibrium properties and relaxation features of a quantum system of N spins antiferromagnetically interacting with each other, with strength J, and coupled to a common bath of bosonic oscillators, with strength α. We show that, in the Ohmic regime, a Beretzinski-Thouless-Kosterlitz quantum phase transition occurs. While for J=0 the critical value of α decreases asymptotically with 1/N by increasing N, for nonvanishing J it turns out to be practically independent on N, allowing to identify a finite range of values of α where spin phase coherence is preserved also for large N. Then, by using matrix product state simulations, and the Mori formalism and the variational approach à la Feynman jointly, we unveil the features of the relaxation, that, in particular, exhibits a nonmonotonic dependence on the temperature reminiscent of the Kondo effect. For the observed quantum phase transition we also establish a criterion analogous to that of the metal-insulator transition in solids.

Optimal parent Hamiltonians for time-dependent states

Rattacaso D., Passarelli G., Mezzacapo A., Lucignano P., Given a generic time-dependent many-body quantum state, we determine the associated parent Hamiltonian. This procedure may require, in general, interactions of any sort. Enforcing the requirement of a fixed set of engineerable Hamiltonians, we find the optimal Hamiltonian once a set of realistic elementary interactions is defined. We provide three examples of this approach. We first apply the optimization protocol to the ground states of the one-dimensional Ising model and a ferromagnetic p-spin model but with time-dependent coefficients. We also consider a time-dependent state that interpolates between a product state and the ground state of a p-spin model. We determine the time-dependent optimal parent Hamiltonian for these states and analyze the capability of this Hamiltonian of generating the state evolution. Finally, we discuss the connections of our approach to shortcuts to adiabaticity.