Transverse laser modes in Bose-Einstein condensates

TL;DR

This paper models the behavior of Bose-Einstein condensates under repeated focusing and loss, revealing formation of Hermite-Gaussian-like modes and vortex generation, analogous to laser resonator dynamics.

Contribution

It introduces a numerical model for trapping and shaping BECs using sequences of off-resonant light pulses, demonstrating mode formation and vortex creation.

Findings

Repeated focusing traps the BEC.

A small proportion of BEC is shaped into Hermite-Gaussian-like modes.

Astigmatic focusing induces vortices.

Abstract

We examine the Bose-Einstein-condensate (BEC) equivalent of transverse aspects of laser resonators. We model numerically repeated focussing of a 2-dimensional BEC, which could be achieved in practice by a series of far off-resonant light pulses. We show for a range of non-linear coefficients that such a series of light pulses traps the BEC. We also model a combination of repeated focussing and loss, which could be achieved with a series of light pulses, some far off-resonant, some resonant. In analogy to light repeatedly being focussed and locally absorbed by passing through a laser resonator, a small proportion (in our model up to 10%) of the BEC is shaped into Hermite-Gaussian-like modes; the remainder of the BEC is lost. This happens irrespective of the presence of a harmonic trap. We show that astigmatic focussing of the resulting Hermite-Gaussian-like modes, which can be achieved by a pair of off-resonant light pulses, results in a specific number of vortices.