Order by Disorder in Spin-Orbit Coupled Bose-Einstein Condensates

TL;DR

This paper studies how quantum and thermal fluctuations select a unique ground state in spin-orbit coupled Bose-Einstein condensates, revealing the order-by-disorder mechanism and its effects on system stability in different dimensions.

Contribution

It provides analytical and numerical analysis demonstrating the order-by-disorder phenomenon in Rashba spin-orbit coupled BECs and explores the stability of the condensate in 2D and 3D.

Findings

Condensation occurs into a single momentum state via order by disorder.

Quantum depletion is small in 3D, thermal depletion diverges logarithmically.

Thermal fluctuations destabilize the 2D condensate.

Abstract

Motivated by recent experiments, we investigate the system of isotropically-interacting bosons with Rashba spin-orbit coupling. At the non-interacting level, there is a macroscopic ground-state degeneracy due to the many ways bosons can occupy the Rashba spectrum. Interactions treated at the mean-field level restrict the possible ground-state configurations, but there remains an accidental degeneracy not corresponding to any symmetry of the Hamiltonian, indicating the importance of fluctuations. By finding analytical expressions for the collective excitations in the long-wavelength limit and through numerical solution of the full Bogoliubov- de Gennes equations, we show that the system condenses into a single momentum state of the Rashba spectrum via the mechanism of order by disorder. We show that in 3D the quantum depletion for this system is small, while the thermal depletion has an infrared logarithmic divergence, which is removed for finite-size systems. In 2D, on the other hand, thermal fluctuations destabilize the system.