Title : Quantum Thermalization and Localization in a Trapped Ion Quantum Simulator
Abstract : When a system thermalizes it loses all local memory of its initial conditions. This is a general feature of open systems and is well described by equilibrium statistical mechanics. Even withina closed (or reversible) quantum system, where the unitary time evolution retains all information about its initial state, subsystems can still thermalize using the rest of the system as an effective heat bath. However, exceptions to thermalization are rare, and in thermal systems the dynamics preceding it are not well understood. Here, we prepare arbitrary non-equilibrium initial states and apply Ising or XY Hamiltonians with long-range interactions and determine if the system thermalizes. In the presence of programmable random disorder we observe two signatures of a many-bodylocalized state: memory retention of the initial conditions and entanglement growth at long times. For sufficiently long-range interactions we fi nd quasi-stationary prethermal behavior. These experiments demonstrate quantum control exerted over trapped ions that will soon allow quantum simulation that cannot be modeled classically.