Fast rotating Bose-Einstein condensates in an asymmetric trap

TL;DR

This paper analyzes how anisotropy in a harmonic trap affects fast rotating Bose-Einstein condensates, revealing two distinct regimes with different vortex and density behaviors, including the emergence of new phenomena at high velocities.

Contribution

It introduces a detailed analysis of anisotropic effects on rotating BECs, identifying two velocity regimes and characterizing their vortex structures and density profiles.

Findings

Hexagonal Abrikosov lattice in the first regime

Vortex-free bulk in the high-velocity regime

Inverted parabola and Gaussian density profiles

Abstract

We investigate the effect of the anisotropy of a harmonic trap on the behaviour of a fast rotating Bose-Einstein condensate. This is done in the framework of the 2D Gross-Pitaevskii equation and requires a symplectic reduction of the quadratic form defining the energy. This reduction allows us to simplify the energy on a Bargmann space and study the asymptotics of large rotational velocity. We characterize two regimes of velocity and anisotropy; in the first one where the behaviour is similar to the isotropic case, we construct an upper bound: a hexagonal Abrikosov lattice of vortices, with an inverted parabola profile. The second regime deals with very large velocities, a case in which we prove that the ground state does not display vortices in the bulk, with a 1D limiting problem. In that case, we show that the coarse grained atomic density behaves like an inverted parabola with large radius in the deconfined direction but keeps a fixed profile given by a Gaussian in the other direction. The features of this second regime appear as new phenomena.