Understanding various phenomena in nonequilibrium dynamics of closed quantum many-body systems, such as quantum thermalization, information scrambling, and nonergodic dynamics, is crucial for modern physics. Using a ladder-type superconducting quantum processor, we perform analog quantum simulations of both the XX-ladder model and the one-dimensional XX model. By measuring the dynamics of local observables, entanglement entropy, and tripartite mutual information, we signal quantum thermalization and information scrambling in the XX ladder. In contrast, we show that the XX chain, as free fermions on a one-dimensional lattice, fails to thermalize to the Gibbs ensemble, and local information does not scramble in the integrable channel. Our experiments reveal ergodicity and scrambling in the controllable qubit ladder, and open the door to further investigations on the thermodynamics and chaos in quantum many-body systems.
Understanding various phenomena in nonequilibrium dynamics of closed quantum many-body systems, such as quantum thermalization, information scrambling, and nonergodic dynamics, is crucial for modern physics. Using a ladder-type superconducting quantum processor, we perform analog quantum simulations of both the XX-ladder model and the one-dimensional XX model. By measuring the dynamics of local observables, entanglement entropy, and tripartite mutual information, we signal quantum thermalization and information scrambling in the XX ladder. In contrast, we show that the XX chain, as free fermions on a one-dimensional lattice, fails to thermalize to the Gibbs ensemble, and local information does not scramble in the integrable channel. Our experiments reveal ergodicity and scrambling in the controllable qubit ladder, and open the door to further investigations on the thermodynamics and chaos in quantum many-body systems.
Understanding how quantum matter behaves when driven out of equilibrium is one of the key focuses in quantum physics. Thanks to impressive progress in the control and precision achieved in quantum synthetic matter over the past decades, the nonequilibrium quantum many-body physics has become one of the most active research areas today, especially after the experimental realization of Bose-Einstein condensates and optical lattices, which allows us to directly observe and study nonequilibrium quantum matter with great accuracy and controllability. In this dissertation, I explore the rich landscape of nonequilibrium quantum many-body physics and how quantum phase transitions, both symmetry-breaking and topological, can be extended to the nonequilibrium setting. In the first part of the dissertation, I focus on spinor Bose-Einstein condensates as an isolated quantum many-body system, and reveal their various dynamical behaviors, including quantum collapse and revivals, thermalization and nonthermal equilibration with no revival even though the system has finite degrees of freedom. In contrast to typical integrable systems, which usually do not thermalize, we find that spinor condensates have a parameter range in which the system thermalizes via the Eigenstate Thermalization Hypothesis (ETH). We show that this observation is linked to the presence of rare nonthermal states whose fraction vanishes with system size, and contributes to the notion of thermalization via weak ETH. Next, I explore a dynamical process that is complementary to thermalization in isolated quantum systems: information scrambling, which could be probed via out-of-time-order correlators (OTOC). I propose a nonintegrable, disordered and quasi-1D spin model, the ladder-XX model, for a feasible detection of information scrambling in a cold atom simulator. This chapter poses a fundamental question: "What are the signatures of quantum phases and phase transitions in isolated interacting systems driven out-of-equilibrium?" I study the ladder-XX model in both clean and disordered potentials, and characterize different nonequilibrium phases, i.e., ergodic and many-body localized, of the model based on the decay properties of OTOCs. Emergent light cone shows sublinear behavior, while the butterfly cones drastically differ from the light cone by demonstrating superlinear spread of information with a velocity that is bounded by the light cone velocity. In the second part of the dissertation, I continue to search for answers to the question posed above, however this time with a particular focus on symmetry-breaking and topological quantum phase transitions. I pin down a universal mechanism underlying the relation between information scrambling at any temperature and quantum phases at low temperatures. Our method points to key ingredients to dynamically detect long-range order in gapped phases through OTOCs for symmetry-breaking quantum phase transitions and Z2 topological order associated with Majorana zero modes localized at the edges. Our results pave the way to an intriguing observation that phases of quantum matter could protect the information from scrambling and thermalization, even when the system is interacting and nonintegrable. Finally, I explore and propose utilizing short-time transient temporal regimes and single-site probes to detect the phases and phase transitions in quantum matter. These studies reveal a dynamical crossover and a dynamical phase transition, respectively for periodic and open-boundary chains. In both cases, a nonequilibrium scaling law appears in the vicinity of the crossover/transition with associated exponents that differ from the analytical predictions for long times. Feasibility of detecting such dynamical criticality in experimental systems are discussed.
Quantum information scrambling under the dynamics of a closed many-body system is of wide interest. The tripartite mutual information (TMI) can quantify the scrambling via its stable negative value under temporal evolution. Here, we study the quench dynamics of the TMI in a nonintegrable Ising model with different initial states in the regimes of strong and weak thermalization. Our numerical results show that the most efficient scrambling can occur when the inverse temperatures of initial states are near zero and in the regime of strong thermalization, and weak thermalization accompanies slow scrambling. We then present an experimental protocol for observing strong and weak thermalization in a one-dimensional array of superconducting qubits, based on which the relation between scrambling and the degree of thermalization revealed in this work can be directly verified by superconducting quantum simulators. The inevitable decoherence effects in real situations are also analyzed, paving the way for faithful quantum simulations on actual experimental platforms.
Quantum information scrambling has received tremendous attention owing to its key concept in the fields of quantum chaos and quantum gravity. Here, with exploiting a fully controllable superconducting quantum processor, we study the verified scrambling in a 1D spin chain by an analog superconducting quantum simulator with the signs and values of individual driving and coupling terms fully controllable. By engineering opposite Hamiltonians on two subsystems, we measure the temporal and spatial patterns of out-of-time ordered correlators (OTOC), with the Hamiltonian mismatch and the decoherence extracted quantitatively from the scrambling dynamics, providing a benchmarking tool for probing not only the spatial but the temporal patterns of scrambling dynamics in many-body systems. Our work demonstrates the superconducting system with strong controllability as a powerful quantum simulator.
Out-of-time-order correlators (OTOCs), recently at the center of discussion on quantum chaos, are tools to understand the information scrambling in different phases of quantum many-body systems. We propose a disordered ladder spin model, the XX ladder, which can be designed in a scalable cold atom setup to detect OTOCs with a sign reversal protocol alternative to existing approaches for evolution backward in time. We study both the clean and disordered XX ladder and characterize different phases (ergodic and many-body localized phases) of the model based on the decay properties of OTOCs. The emergent effective lightcone shows sublinear behavior, while the butterfly cones drastically differ from the lightcone via demonstrating superlinear behavior. Based on our results, one can observe how the information scrambling changes in the transition from well-studied one-dimensional spin models to unexplored two-dimensional spin models in a local setting.
A closed quantum system never forgets its initial state, but the encoded information can get scrambled and become inaccessible without measuring a large fraction of all the system degrees of freedom. This scrambling can be diagnosed by studying the spatial spreading of initially local operators under the Heisenberg time evolution, and the decay of the out-of-time-ordered correlators (OTOC). What insights can OTOCs provide to understand the dynamics of quantum many-body systems? What are the characteristic behaviors of OTOCs during the time evolution? How is information scrambling affected by the dissipation in open quantum many-body systems? We first study slow scrambling in many-body localized systems via calculating various correlators, two-point retarded correlators and OTOCs. Comparing with retarded correlators, OTOCs provide more information about the dynamics. We find that disorder slows and partially halts the onset of information scrambling. Instead of ballistic spreading, propagation of information forms a logarithmic light cone. Next, we study the finite-size scaling of OTOCs at late times in generic thermalizing quantum many-body systems. When energy is conserved, the late-time saturation value of the OTOC of generic traceless local operators scales as an inverse polynomial in the system size. This is in contrast to the inverse exponential scaling expected for chaotic dynamics without energy conservation. We also study information scrambling in open quantum many-body systems. We define a dissipative version of OTOC and study its behaviors in a prototypical chaotic quantum chain with dissipation. We find that dissipation leads to not only the overall decay of the scrambled information due to leaking, but also structural changes so that the information light cone can only reach a finite distance even when the effect of overall decay is removed. Finally, we construct a family of local Hamiltonians for understanding the asymmetric information scrambling. Our models live on a one-dimensional lattice and exhibit asymmetric butterfly light cone between the left and right spatial directions.
Abstract The shift from reversible quantum dynamics to irreversible thermodynamics is one of the most complex and at the same time the most important issue in modern physics. A new and efficient method developed by studying black holes and quantum chaos gives the problem stance as one of information dynamics. In this paper, the authors explore the scenario whereby information scrambling is viewed as the micro-level power of quantum thermalization. They start by explaining the most basic paradigms of thermalizing systems that are typified by the eigenstate thermalization hypothesis (ETH) and their non-thermalizing opposites which are characterized by many-body localization. Following that, the authors engage in a comprehensive discussion of the out-of-time-order correlator as the primary tool for diagnosing scrambling, giving a detailed account of its connection with operator spreading, quantum chaos, and the butterfly effect. The central idea that unites this review is that fast, exponential scrambling dynamics bring about ETH and thermalization while a slowdown in scrambling results in localization. An extensive review of the pioneering experiments on trapped-ion, superconducting-qubit, and other quantum-simulation platforms that have clearly witnessed these phenomena is conducted. Ultimately, physicists point out the main unresolved questions and future research paths at the meeting point of quantum gravity, condensed matter, and quantum information science, positioning scrambling as a critical concept for the next few years in many-body physics.