A blueprint for experiments exploring the Poincar\'e quantum recurrence theorem

Abstract

The quantum form of the Poincar\'e recurrence theorem stipulates that a system with a time-independent Hamiltonian and discrete energy levels returns arbitrarily close to its initial state in a finite time. Qubit systems, being highly isolated from their dissipative surroundings, provide a possible experimental testbed for studying this theoretical construct. Here we investigate a $N$-qubit system, weakly coupled to its environment. We present quantitative analytical and numerical results on both the revival probability and time, and demonstrate that the system indeed returns arbitrarily close to its initial state in a time exponential in the number of qubits $N$. The revival times become astronomically large for systems with just a few tens of qubits. Given the lifetimes achievable in present-day superconducting multi-qubit systems, we propose a realistic experimental test of the theory and scaling of Poincar\'e revivals. Our study of quantum recurrence provides new insight into how thermalization emerges in isolated quantum systems.