Non-markovian mesoscopic dissipative dynamics of open quantum spin chains

We study the dissipative dynamics of $N$ quantum spins with Lindblad generator consisting of operators scaling as fluctuations, namely with the inverse square-root of $N$. In the large $N$ limit, the microscopic dissipative time-evolution converges to a non-Markovian unitary dynamics on strictly local operators, while at the mesoscopic level of fluctuations it gives rise to a dissipative non-Markovian dynamics. The mesoscopic time-evolution is Gaussian and exhibits either a stable or an unstable asymptotic character; furthermore, the mesoscopic dynamics builds correlations among fluctuations that survive in time even when the original microscopic dynamics is unable to correlate local observables.Comment: 18 page

Entangled time-crystal phase in an open quantum light-matter system

Time-crystals are nonequilibrium many-body phases in which the state of the system dynamically approaches a limit cycle. While these phases are recently in the focus of intensive research, it is still far from clear whether they can host quantum correlations. In fact, mostly classical correlations have been observed so far and time-crystals appear to be effectively classical high-entropy phases. Here, we consider the nonequilibrium behavior of an open quantum light-matter system, realizable in current experiments, which maps onto a paradigmatic time-crystal model after an adiabatic elimination of the light field. The system displays a bistable regime, with coexistent time-crystal and stationary phases, terminating at a tricritical point from which a second-order phase transition line departs. While light and matter are uncorrelated in the stationary phase, the time-crystal phase features bipartite correlations, both of quantum and classical nature. Our work unveils that time-crystal phases in collective open quantum systems can sustain quantum correlations, including entanglement, and are thus more than effectively classical many-body phases.Comment: 8+5 pages, 3+1 figure

Nonequilibrium Phase Transitions in (1+1)-Dimensional Quantum Cellular Automata with Controllable Quantum Correlations

Motivated by recent progress in the experimental development of quantum simulators based on Rydberg atoms, we introduce and investigate the dynamics of a class of (1+1)-dimensional quantum cellular automata. These non-equilibrium many-body models, which are quantum generalisations of the Domany-Kinzel cellular automaton, possess two key features: they display stationary behaviour and non-equilibrium phase transitions despite being isolated systems. Moreover, they permit the controlled introduction of local quantum correlations, which allows for the impact of quantumness on the dynamics and phase transition to be assessed. We show that projected entangled pair state tensor networks permit a natural and efficient representation of the cellular automaton. Here, the degree of quantumness and complexity of the dynamics is reflected in the difficulty of contracting the tensor network

Continuous sensing and parameter estimation with the boundary time-crystal

A boundary time-crystal is a quantum many-body system whose dynamics is governed by the competition between coherent driving and collective dissipation. It is composed of N two-level systems and features a transition between a stationary phase and an oscillatory one. The fact that the system is open allows to continuously monitor its quantum trajectories and to analyze their dependence on parameter changes. This enables the realization of a sensing device whose performance we investigate as a function of the monitoring time T and of the system size N. We find that the best achievable sensitivity is proportional to $\sqrt{T}N$, i.e., it follows the standard quantum limit in time and Heisenberg scaling in the particle number. This theoretical scaling can be achieved in the oscillatory time-crystal phase and it is rooted in emergent quantum correlations. The main challenge is, however, to tap this capability in a measurement protocol that is experimentally feasible. We demonstrate that the standard quantum limit can be surpassed by cascading two time-crystals, where the quantum trajectories of one time-crystal are used as input for the other one

Quantum fluctuations and entanglement in mesoscopic systems

Due to the large amount of microscopic constituents, sensible information that can be gathered about many- body systems concerns usually the behaviour of collective observables; among them, surely average observables, like the mean magnetization in quantum spin chains, but also fluctuations around mean-values. Average operators over all particles are defined with a scaling proportional to the inverse number N of considered particles; in the large N limit, the emergent collective operators form a classical algebra, with no footprints of the microscopic quantum structure they result from. On the contrary, another class of collective observables, the so-called fluctuation operators defined with a scaling proportional to square root of N , has been proved, by means of quantum central limit theorems, to retain quantum properties, giving rise to a Gaussian Bosonic system. These collective observables may thus be interpreted as witnesses of a mesoscopic behaviour positioned at the interface between macroscopic, classical behaviours and microscopic quantum ones, providing a suitable framework where to look for collective quantum phenomena in many-body systems. In this thesis we studied the dynamical behaviour of these fluctuation operators, when the many-body mesoscopic system is considered not to be isolated, but in a weak interaction with a larger environment; this is the most common situation encountered in actual experiments, where these systems can never be thought of as completely isolated from their thermal surroundings. Under some conditions on the dynamical generator, we showed that such dissipative evolution of fluctuations exists and is such that it preserves their Gaussian character. By means of a particular example, we also demonstrated that two non-interacting many-body systems can become entangled, at the level of their fluctuation operators, through the presence of a common environment usually responsible for decoherence and emergence of classical behaviours. Furthermore, the behaviour of such correlations has a neat dependence on the temperature of the heat bath, displaying a sort of phase transition, witnessed by the existence of a finite critical temperature above which entanglement is not possible

Numerical Simulation of Critical Dissipative Non-Equilibrium Quantum Systems with an Absorbing State

The simulation of out-of-equilibrium dissipative quantum many body systems is a problem of fundamental interest to a number of fields in physics, ranging from condensed matter to cosmology. For unitary systems, tensor network methods have proved successful and extending these to open systems is a natural avenue for study. In particular, an important question concerns the possibility of approximating the critical dynamics of non-equilibrium systems with tensor networks. Here, we investigate this by performing numerical simulations of a paradigmatic quantum non-equilibrium system with an absorbing state: the quantum contact process. We consider the application of matrix product states and the time-evolving block decimation algorithm to simulate the time-evolution of the quantum contact process at criticality. In the Lindblad formalism, we find that the Heisenberg picture can be used to improve the accuracy of simulations over the Schrodinger approach, which can be understood by considering the evolution of operator-space entanglement. Furthermore, we also consider a quantum trajectories approach, which we find can reproduce the expected universal behaviour of key observables for a significantly longer time than direct simulation of the average state. These improved results provide further evidence that the universality class of the quantum contact process is not directed percolation, which is the class of the classical contact process

Thermalization with a multibath: an investigation in simple models

We study analytically and numerically a couple of paradigmatic spin models, each described in terms of two sets of variables attached to two different thermal baths with characteristic timescales $T$ and $\tau$ and inverse temperatures $B$ and $\beta$. In the limit in which one bath becomes extremely slow ($\tau \to \infty$), such models amount to a paramagnet and to a one-dimensional ferromagnet, in contact with a single bath. We show that these systems reach a stationary state in a finite time for any choice of $B$ and $\beta$. We determine the non-equilibrium fluctuation-dissipation relation between the autocorrelation and the response function in such state and, from that, we discuss if and how thermalization with the two baths occurs and the emergence of a non-trivial fluctuation-dissipation ratio.Comment: 15 pages, 6 figure

Universal and nonuniversal probability laws in Markovian open quantum dynamics subject to generalized reset processes

We consider quantum jump trajectories of Markovian open quantum systems subject to stochastic in time resets of their state to an initial configuration. The reset events provide a partitioning of quantum trajectories into consecutive time intervals, defining sequences of random variables from the values of a trajectory observable within each of the intervals. For observables related to functions of the quantum state, we show that the probability of certain orderings in the sequences obeys a universal law. This law does not depend on the chosen observable and, in case of Poissonian reset processes, not even on the details of the dynamics. When considering (discrete) observables associated with the counting of quantum jumps, the probabilities in general lose their universal character. Universality is only recovered in cases when the probability of observing equal outcomes in a same sequence is vanishingly small, which we can achieve in a weak reset rate limit. Our results extend previous findings on classical stochastic processes [N.~R.~Smith et al., EPL {\bf 142}, 51002 (2023)] to the quantum domain and to state-dependent reset processes, shedding light on relevant aspects for the emergence of universal probability laws.Comment: 13 pages, 5 figure