Attractive Bose-Einstein Condensates in three dimensions under rotation: Revisiting the problem of stability of the ground state in harmonic traps

TL;DR

This paper investigates the stability of attractive Bose-Einstein condensates in three-dimensional harmonic traps under rotation, finding that rotation does not delay collapse and the system's properties remain largely unchanged.

Contribution

It provides a detailed analysis of the collapse threshold of attractive BECs under rotation using many-body and Gross-Pitaevskii approaches, challenging previous findings.

Findings

Rotation does not postpone collapse in attractive BECs.

Properties of attractive BECs are unaffected by rotation in isotropic traps.

Collapse threshold remains unchanged under rotation.

Abstract

We study harmonically trapped ultracold Bose gases with attractive interparticle interactions under external rotation in three spatial dimensions and determine the critical value of the attraction strength where the gas collapses as a function of the rotation frequency. To this end we examine the stationary state in the corotating frame with a many-body approach as well as within the Gross-Pitaevskii theory of systems in traps with different anisotropies. In contrast to recently reported results [N. A. Jamaludin, N. G. Parker, and A. M. Martin, Phys. Rev. A \textbf{77}, 051603(R) (2008)], we find that the collapse is not postponed in the presence of rotation. Unlike repulsive gases, the properties of the attractive system remain practically unchanged under rotation in isotropic and slightly anisotropic traps.