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Closed quantum many-body systems out of equilibrium pose several long-standing problems in physics. Recent years have seen a tremendous progress in approaching these questions, not least due to experiments with cold atoms and trapped ions in instances of quantum simulations. This article provides an overview on the progress in understanding dynamical equilibration and thermalisation of closed quantum many-body systems out of equilibrium due to quenches, ramps and periodic driving. It also addresses topics such as the eigenstate thermalisation hypothesis, typicality, transport, many-body localisation, universality near phase transitions, and prospects for quantum simulations.
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Certain wave functions of non-interacting quantum chaotic systems can exhibit scars in the fabric of their real-space density profile. Quantum scarred wave functions concentrate in the vicinity of unstable periodic classical trajectories. We introduce the notion of many-body quantum scars which reflect the existence of a subset of special many-body eigenstates concentrated in certain parts of the Hilbert space. We demonstrate the existence of scars in the Fibonacci chain -- the one- dimensional model with a constrained local Hilbert space realized in the 51 Rydberg atom quantum simulator [H. Bernien et al., arXiv:1707.04344]. The quantum scarred eigenstates are embedded throughout the thermalizing many-body spectrum, but surprisingly lead to direct experimental signatures such as robust oscillations following a quench from a charge-density wave state found in experiment. We develop a model based on a single particle hopping on the Hilbert space graph, which quantitatively captures the scarred wave functions up to large systems of L = 32 atoms. Our results suggest that scarred many-body bands give rise to a new universality class of quantum dynamics, which opens up opportunities for creating and manipulating novel states with long-lived coherence in systems that are now amenable to experimental study.
Recent discovery of persistent revivals in quantum simulators based on Rydberg atoms have pointed to the existence of a new type of dynamical behavior that challenged the conventional paradigms of integrability and thermalization. This novel collective effect has been named quantum many-body scars by analogy with weak ergodicity breaking of a single particle inside a stadium billiard. In this overview, we provide a pedagogical introduction to quantum many-body scars and highlight the newly emerged connections with the semiclassical quantization of many-body systems. We discuss the relation between scars and more general routes towards weak violations of ergodicity due to embedded algebras and non-thermal eigenstates, and highlight possible applications of scars in quantum technology.
In statistical mechanics, a small system exchanges conserved quantities---heat, particles, electric charge, etc.---with a bath. The small system thermalizes to the canonical ensemble, or the grand canonical ensemble, etc., depending on the conserved quantities. The conserved quantities are represented by operators usually assumed to commute with each other. This assumption was removed within quantum-information-theoretic (QI-theoretic) thermodynamics recently. The small systems long-time state was dubbed ``the non-Abelian thermal state (NATS). We propose an experimental protocol for observing a system thermalize to the NATS. We illustrate with a chain of spins, a subset of which form the system of interest. The conserved quantities manifest as spin components. Heisenberg interactions push the conserved quantities between the system and the effective bath, the rest of the chain. We predict long-time expectation values, extending the NATS theory from abstract idealization to finite systems that thermalize with finite couplings for finite times. Numerical simulations support the analytics: The system thermalizes to the NATS, rather than to the canonical prediction. Our proposal can be implemented with ultracold atoms, nitrogen-vacancy centers, trapped ions, quantum dots, and perhaps nuclear magnetic resonance. This work introduces noncommuting conserved quantities from QI-theoretic thermodynamics into quantum many-body physics: atomic, molecular, and optical physics and condensed matter.
The assumption that quantum systems relax to a stationary state in the long-time limit underpins statistical physics and much of our intuitive understanding of scientific phenomena. For isolated systems this follows from the eigenstate thermalization hypothesis. When an environment is present the expectation is that all of phase space is explored, eventually leading to stationarity. Notable exceptions are decoherence-free subspaces that have important implications for quantum technologies and have so far only been studied for systems with a few degrees of freedom. Here we identify simple and generic conditions for dissipation to prevent a quantum many-body system from ever reaching a stationary state. We go beyond dissipative quantum state engineering approaches towards controllable long-time non-stationarity typically associated with macroscopic complex systems. This coherent and oscillatory evolution constitutes a dissipative version of a quantum time-crystal. We discuss the possibility of engineering such complex dynamics with fermionic ultracold atoms in optical lattices.
Chaotic quantum many-body dynamics typically lead to relaxation of local observables. In this process, known as quantum thermalization, a subregion reaches a thermal state due to quantum correlations with the remainder of the system, which acts as an intrinsic bath. While the bath is generally assumed to be unobserved, modern quantum science experiments have the ability to track both subsystem and bath at a microscopic level. Here, by utilizing this ability, we discover that measurement results associated with small subsystems exhibit universal random statistics following chaotic quantum many-body dynamics, a phenomenon beyond the standard paradigm of quantum thermalization. We explain these observations with an ensemble of pure states, defined via correlations with the bath, that dynamically acquires a close to random distribution. Such random ensembles play an important role in quantum information science, associated with quantum supremacy tests and device verification, but typically require highly-engineered, time-dependent control for their preparation. In contrast, our approach uncovers random ensembles naturally emerging from evolution with a time-independent Hamiltonian. As an application of this emergent randomness, we develop a benchmarking protocol which estimates the many-body fidelity during generic chaotic evolution and demonstrate it using our Rydberg quantum simulator. Our work has wide ranging implications for the understanding of quantum many-body chaos and thermalization in terms of emergent randomness and at the same time paves the way for applications of this concept in a much wider context.
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