Spontaneous symmetry breaking in coupled Bose-Einstein condensates

TL;DR

This paper proves that two coupled Bose-Einstein condensates exhibit spontaneous symmetry breaking of their relative phase in the infinite volume limit, providing a rigorous foundation for observable interference phenomena.

Contribution

It establishes a rigorous proof of spontaneous symmetry breaking of the relative U(1) phase in coupled Bose-Einstein condensates, linking it to quantum antiferromagnet theory.

Findings

Spontaneous symmetry breaking occurs in the coupled system.

The relative U(1) phase is well-defined and observable.

The proof leverages low-lying states and SSB theory from quantum antiferromagnets.

Abstract

We study a system of two hardcore bosonic Hubbard models weakly coupled with each other by tunneling. Assuming that the single uncoupled model exhibits off-diagonal long-range order, we prove that the coupled system exhibits spontaneous symmetry breaking (SSB) in the infinite volume limit, in the sense that the two subsystems maintain a definite relative U(1) phase when the tunneling is turned off. Although SSB of the U(1) phase is never observable in a single system, SSB of the relative U(1) phase is physically meaningful and observable by interference experiments. The present theorem is made possible by the rigorous theory of low-lying states and SSB in quantum antiferromagnets developed over the years.