Entanglement Pre-thermalization in an Interaction Quench between Two Harmonic Oscillators

TL;DR

This paper investigates entanglement pre-thermalization in a simple model of two harmonic oscillators after an interaction quench, revealing how subsystems thermalize while the total system remains entangled, and how perturbations affect this state.

Contribution

The study demonstrates that a generalized Gibbs ensemble accurately describes the total system during entanglement pre-thermalization in a harmonic oscillator model.

Findings

Subsystems reach thermal-like states while the total system remains entangled.

A generalized Gibbs ensemble captures the total system's state.

Perturbations shorten the lifetime of entanglement pre-thermalization.

Abstract

Entanglement pre-thermalization (EP) is a quasi-stationary nonequilibrium state of a composite system in which each individual subsystem looks thermal but the entire system remains nonthermal due to quantum entanglement between subsystems. We theoretically study the dynamics of EP following a coherent split of a one-dimensional harmonic potential in which two interacting bosons are confined. This problem is equivalent to that of an interaction quench between two harmonic oscillators. We show that this simple model captures the bare essentials of EP; that is, each subsystem relaxes to an approximate thermal equilibrium, whereas the total system remains entangled. We find that a generalized Gibbs ensemble, which incorporates nonlocal conserved quantities, exactly describes the total system. In the presence of a symmetry-breaking perturbation, EP is quasi-stationary and eventually reaches thermal equilibrium. We analytically show that the lifetime of EP is inversely proportional to the magnitude of the perturbation.