Ergodic dynamics and thermalization in an isolated quantum system

TL;DR

This paper demonstrates ergodic behavior in a small, controllable quantum system of three superconducting qubits, linking quantum entanglement dynamics with classical chaos and thermodynamics.

Contribution

It provides experimental evidence of ergodic dynamics in a minimal quantum system, connecting quantum entanglement with classical phase space behavior.

Findings

Full system acts as a reservoir for individual qubits

Higher entanglement entropy correlates with classical chaos

System exhibits ergodic dynamics in high-entropy regions

Abstract

Statistical mechanics is founded on the assumption that all accessible configurations of a system are equally likely. This requires dynamics that explore all states over time, known as ergodic dynamics. In isolated quantum systems, however, the occurrence of ergodic behavior has remained an outstanding question. Here, we demonstrate ergodic dynamics in a small quantum system consisting of only three superconducting qubits. The qubits undergo a sequence of rotations and interactions and we measure the evolution of the density matrix. Maps of the entanglement entropy show that the full system can act like a reservoir for individual qubits, increasing their entropy through entanglement. Surprisingly, these maps bear a strong resemblance to the phase space dynamics in the classical limit; classically chaotic motion coincides with higher entanglement entropy. We further show that in regions of high entropy the full multi-qubit system undergoes ergodic dynamics. Our work illustrates how controllable quantum systems can investigate fundamental questions in non-equilibrium thermodynamics.