Ergodic dynamics and thermalization in an isolated quantum system - Charles Neill

Statistical mechanics is founded on the assumption that all accessible states of a system are equally likely. This requires dynamics that explore all configurations over time, known as ergodic dynamics. Here, using three fully-coupled superconducting qubits, we demonstrate ergodic dynamics and the resulting thermalization. We subject the qubits to a sequence of periodic rotations and interactions and measure the density matrix as a function of time. We find a striking resemblance between maps of the entanglement entropy and the phase space dynamics in the classical limit; classically chaotic regions coincide with regions of nearly maximum entanglement entropy. We further show that in regions with high entropy the qubits explore the entire accessible state space, demonstrating quantum ergodic dynamics. In these regions, the time-averaged density matrix approaches a microcanonical ensemble. Our work illustrates how fundamental questions in non-equilibrium thermodynamics can be studied using superconducting circuits.