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.
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.
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.
We characterize nonequilibrium phases in long-range dissipative spin systems through the statistical properties of quantum jump trajectories. While the average dynamics governed by the Lindblad master equation provides access to steady-state expectation values of order parameters, the quantum trajectory framework reveals features encoded in the spatial and temporal correlations of detection events. Focusing on a model exhibiting a paramagnetic-to-ferromagnetic phase transition, we investigate the full counting statistics of quantum jumps using a tilted Lindbladian approach. We combine this with cluster mean-field and cumulant expansion techniques, which allow us to capture, respectively, the short- and long-range structure of jump correlations. In addition, we study the waiting-time distributions of detection events. We show that quantum jump correlations display clear signatures of the underlying phases and reveal distinct dynamical features across the transition. Our results highlight the potential of trajectory-resolved observables as probes of collective behavior in open quantum many-body systems and provide new insights into the role of long-range interactions in shaping nonequilibrium dynamics.
Quantum states in complex aggregates are unavoidably affected by environmental effects, which typically cannot be accurately modeled by simple Markovian processes. As system sizes scale up, nonperturbative simulation becomes thus unavoidable, but they are extremely challenging due to the intimate interplay of intrinsic many-body interaction and time-retarded feedback from environmental degrees of freedom. In this work, we utilize the recently developed quantum dissipation with minimally extended state space approach to address reservoir induced long-ranged temporal correlations in finite size Ising-type spin chains. For thermal reservoirs with ohmic and subohmic spectral density, we simulate the quantum time evolution from finite to zero temperature. The competition between thermal fluctuations, quantum fluctuations, and anti-/ferromagnetic interactions reveals a rich pattern of dynamical phases, including dissipative induced phase transitions and spatiotemporal correlations.
We investigate the dynamical spreading of correlations in many-body quantum systems with competing short- and global-range couplings. We monitor the nonequilibrium dynamics of the correlations following a quench, showing that for strong short-range couplings the propagation of correlations is dominated at short and intermediate distances by a causal, light-cone dynamics, resembling the purely short-range quantum systems. However, the interplay of short- and global-range couplings leads to a crossover between space-time regions in which the light cone persists to regions where a supersonic, distance-independent spreading of the correlations occurs. We identify the important ingredients needed for capturing the supersonic spreading and demonstrate our findings in systems of interacting bosonic atoms, in which the global-range coupling is realized by a coupling to a cavity light field or atomic long-range interactions, respectively. We show that our results hold in both one and two dimensions and in the presence of dissipation. Furthermore, we characterize the short-time power-law scaling of the distance-independent growth of the density-density correlations.
We study the long-time dynamics of a dissipative Ising chain with varying quantum correlation. Invoking an ensemble-average formalism and assuming spatial translation symmetry, we show that the dynamics can be described by a Lindblad master equation with an interpolated coherent Hamiltonian. In the classical limit, the interpolation Hamiltonian leads to a set of nonlinear equations of motion, where limit cycles can emerge in the long-time dynamics. In the quantum limit, by contrast, the system approaches a ferromagnetic steady state at long times. In between the two extremes, the discrete spatial translation symmetry can be spontaneously broken, as an antiferromagnetic steady state emerges, bridging the classical and quantum regimes. In particular, we illustrate how the classical limit-cycle behavior gradually disappears with the increase of quantum correlation. Since our model in the two extremes respectively applies to a dissipative Rydberg gas in the high- and zero-temperature limits, we expect it to provide a qualitatively correct description of dissipative Rydberg gases at interim temperatures and shed light on the fate of limit cycles in a quantum open system.
The study of many-body quantum physics has been recently challenged by the appearance of an increasing number of experimental platforms where genuine quantum phenomena take place notwithstanding the presence of an environment and of dissipation. Exciton-polaritons, lossy atomic and molecular gases, cavity QED arrays, arrays of trapped ions and Rydberg atoms, are only few prominent examples of a long list. The present work is ideally divided into two parts, the former is devoted to methodological results; the latter to the theoretical characterization of experimental data. Whereas the notion of equilibrium has been a fruitful guide to the development of standard many-body physics, these setups are inherently out of equilibrium and their modelisation requires the introduction of new theoretical tools. Several methods for addressing this dissipative out-of-equilibrium dynamics have been proposed, based for instance on quantum trajectories, truncated Wigner expansions, tensor networks, machine learning, but the solution of many-body physics for open quantum systems remains a formidable task. Clearly, techniques developed in the framework of Hamiltonian closed systems are a continuous source of inspiration for novel developments, and in this work we present the generalization of one such technique, the so-called flow equations, to the dissipative framework where the generator of the dynamics is a linear non-Hermitian operator; notable examples include non-Hermitian Hamiltonians and Lindblad master equations. In the second part of this work we focus on two-body lossy dynamics in strongly-correlated cold atomic gases. In particular, we derive an effective description for the long-time dynamics of a spin ½ fermionic system by extending a pre-existing theory for the bosonic case.