Emergent Symmetry at Superradiance Transition of a Bose Condensate in Two Crossed Beam Cavities

TL;DR

This paper explains the emergence of an additional U(1) symmetry at the superradiant transition in a Bose condensate within two crossed beam cavities, revealing conditions for its appearance and implications for the nature of the phase transition.

Contribution

The paper identifies conditions for emergent U(1) symmetry at the superradiant transition and connects these to recent experimental observations, showing how the transition can become first order.

Findings

Emergent U(1) symmetry appears near the superradiant transition.

The symmetry is not present in the full Hamiltonian but arises under specific conditions.

Tuning system parameters can change the transition from second to first order.

Abstract

Recently the ETH group has reported an experiment on superradiant transition of a Bose condensate in two crossed beam cavities. The surprise is that they find that across the superradiant transition, the cavity light can be emitted in any superposition of these two cavity modes. This indicates an additional $U(1)$ symmetry that does not exist in the full Hamiltonian. In this letter we show that this symmetry is an emergent symmetry in the vicinity of the phase transition. We identify all the necessary conditions that are required for this emergent $U(1)$ symmetry and show that the ETH experiment is a special case that satisfies these conditions. We further show that the superradiant transition in this system can also be driven to a first order one when the system is tuned away from the point having the emergent symmetry.