Bose-Einstein condensates in toroidal traps: instabilities, swallow-tail loops, and self-trapping

TL;DR

This paper investigates the stability, dynamics, and nonlinear phenomena such as swallow-tail loops and self-trapping in a rotating Bose-Einstein condensate confined in a toroidal trap, revealing connections to double-well systems.

Contribution

It provides a detailed analysis of stability regions, instabilities, and the emergence of hysteresis and self-trapping phenomena in a rotating toroidal BEC, linking these to energy level structures.

Findings

Identification of stability and instability regions for different interactions.

Observation of swallow-tail loops indicating hysteresis during rotation.

Demonstration of macroscopic quantum self-trapping linked to energy level behavior.

Abstract

We study the stability and dynamics of an ultra-cold bosonic gas trapped in a toroidal geometry and driven by rotation, in the absence of dissipation. We first delineate, via the Bogoliubov mode expansion, the regions of stability and the nature of instabilities of the system for both repulsive and attractive interaction strengths. To study the response of the system to variations in the rotation rate, we introduce a "disorder" potential, breaking the rotational symmetry. We demonstrate the breakdown of adiabaticity as the rotation rate is slowly varied and find forced tunneling between the system's eigenstates. The non-adiabaticity is signaled by the appearance of a swallow-tail loop in the lowest-energy level, a general sign of hysteresis. Then, we show that this system is in one-to-one correspondence with a trapped gas in a double-well potential and thus exhibits macroscopic quantum self-trapping. Finally, we show that self-trapping is a direct manifestation of the behavior of the lowest-energy level.