Designing non-equilibrium states of quantum matter through stochastic resetting

Abstract

We consider closed quantum many-body systems subject to stochastic resetting. This means that their unitary time evolution is interrupted by resets at randomly selected times. When a reset takes place the system is reinitialized to a state chosen from a set of reset states conditionally on the outcome of a measurement taken immediately before resetting. We construct analytically the resulting non-equilibrium stationary state, thereby establishing an explicit connection between quantum quenches in closed systems and the emergent open system dynamics induced by stochastic resetting. We discuss as an application the paradigmatic transverse-field quantum Ising chain. We show that signatures of its ground-state quantum phase transition are visible in the steady state of the reset dynamics as a sharp crossover. Our findings show that a controlled stochastic resetting dynamics allows to design non-equilibrium stationary states of quantum many-body systems, where uncontrolled dissipation and heating can be prevented. These states can thus be created on demand and exploited, e.g., as a resource for quantum enhanced sensing on quantum simulator platforms.

23 pages. 6 pages main text and 17 pages supplemental material

References in corpus (22)

• Single-Atom Resolved Fluorescence Imaging of an Atomic Mott Insulator
• Many-Body Physics with Individually-Controlled Rydberg Atoms
• Quantum Quench in the Transverse Field Ising Chain
• Stochastic Resetting and Applications
• Observation of mesoscopic crystalline structures in a two-dimensional Rydberg gas
• First Passage Under Restart
• The Statistics of the Work Done on a Quantum Critical System by Quenching a Control Parameter
• Quench dynamics across quantum critical points
• Diffusion with resetting in arbitrary spatial dimension
• Quantum Quench in the Transverse Field Ising Chain II: Stationary State Properties
• Dynamical transition in the temporal relaxation of stochastic processes under resetting
• Dynamical Correlations after a Quantum Quench
• Monotonous continuous-time random walks with drift and stochastic reset events
• Quantum relaxation after a quench in systems with boundaries
• Quasilocalized dynamics from confinement of quantum excitations
• Ising model with stochastic resetting
• Real-time dynamics of string breaking in quantum spin chains
• First detected arrival of a quantum walker on an infinite line
• Controlling particle currents with evaporation and resetting from an interval
• Confinement and bound states of bound states in a transverse-field two-leg Ising ladder
• Dynamical crossover in the transient quench dynamics of short-range transverse field Ising models
• Confinement in the spectrum of a Heisenberg-Ising spin ladder