Stability of the quantized circulation of an attractive Bose-Einstein condensate in a rotating torus

TL;DR

This paper studies the rotational behavior of attractive Bose-Einstein condensates in a torus, analyzing ground states, circulation quantization, and thermal effects, with theoretical and numerical methods to understand stability and transitions.

Contribution

It provides analytical solutions for ground states, compares Bogoliubov theory with exact diagonalization, and explores thermal and symmetry-breaking effects on circulation stability.

Findings

Quantization of circulation exists in uniform states but not in solitons.

Bogoliubov theory accurately predicts zero-temperature properties.

Thermal fluctuations can smear circulation plateaus.

Abstract

We investigate rotational properties of a system of bosons with attractive interactions confined in a one-dimensional torus. Two kinds of ground states, uniform-density and bright-soliton states, are obtained analytically as functions of the strength of interaction and of the rotational frequency of the torus. The quantization of circulation appears in the uniform-density state, but disappears upon formation of the soliton. By comparison with the results of exact diagonalization of the many-body Hamiltonian, we show that the Bogoliubov theory is valid at absolute zero over a wide range of parameters. At finite temperature we employ the exact diagonalization method to examine how thermal fluctuations smear the plateaus of the quantized circulation. Finally, by rotating the system with an axisymmetry-breaking potential, we clarify the process in which the quantized circulation becomes thermodynamically stabilized.