Bosons in anisotropic traps: ground state and vortices

TL;DR

This paper solves the Gross-Pitaevskii equations for Bose-Einstein condensates in anisotropic traps, analyzing ground states, vortex formation, and stability, with comparisons to experimental data and approximate models.

Contribution

It provides detailed solutions for condensate properties in anisotropic traps, including vortex states and stability analysis, extending previous models with new computational results.

Findings

Vortex states increase condensate stability with attractive interactions.

Calculated critical angular velocities for vortex formation.

Compared theoretical results with experimental estimates for $^{87}$Rb.

Abstract

We solve the Gross-Pitaevskii equations for a dilute atomic gas in a magnetic trap, modeled by an anisotropic harmonic potential. We evaluate the wave function and the energy of the Bose Einstein condensate as a function of the particle number, both for positive and negative scattering length. The results for the transverse and vertical size of the cloud of atoms, as well as for the kinetic and potential energy per particle, are compared with the predictions of approximated models. We also compare the aspect ratio of the velocity distribution with first experimental estimates available for $^{87}$Rb. Vortex states are considered and the critical angular velocity for production of vortices is calculated. We show that the presence of vortices significantly increases the stability of the condensate in the case of attractive interactions.