Sign of tunnel coupling in barrier-separated Bose-Einstein condensates and stability of double-ring systems

TL;DR

This paper clarifies the stability of barrier-separated Bose-Einstein condensates, showing that the non-rotating ground state remains stable regardless of tunnel coupling, and discusses the sign of the tunnel coupling in such systems.

Contribution

It provides a revised analysis demonstrating the stability of non-rotating states and clarifies the sign of tunnel coupling in double-ring Bose-Einstein condensates.

Findings

Non-rotating ground state is stable for all tunnel coupling values.

Excited states with π phase difference are unstable due to snake instability.

The tunnel coupling through the barrier is always negative for physical systems.

Abstract

We revisit recent claims about the instability of non-rotating tunnel coupled annular Bose-Einstein condensates leading to the emergence of angular-momentum Josephson oscillation [Phys. Rev. Lett. 98, 050401 (2007), arXiv:quant-ph/0609133v2]. It was predicted that all stationary states with uniform density become unstable in certain parameter regimes. By careful analysis, we arrive at a different conclusion. We show that there is a stable non-rotating and uniform ground state for any value of the tunnel coupling and repulsive interactions. The instability of an excited state with $\pi$ phase difference between the condensates can be interpreted in terms of the familiar snake instability. We further discuss the sign of the tunnel coupling through a separating barrier, which carries significance for the nature of the stationary states. It is found to always be negative for physical reasons.