Resonant Generation of Topological Modes in Trapped Bose Gases

TL;DR

This paper develops a comprehensive theory for resonant generation of topological modes in trapped Bose gases, including multiple-mode formation, stability, and nonlinear effects, supported by analytical and numerical methods.

Contribution

It generalizes the theory of resonant mode generation in Bose-Einstein condensates, incorporating multiple modes, shape constraints, and nonlinear phenomena.

Findings

Multiple topological modes can be generated resonantly.

Stability regions for the modes are identified.

Harmonic generation and parametric conversion effects are predicted.

Abstract

Trapped Bose atoms cooled down to temperatures below the Bose-Einstein condensation temperature are considered. Stationary solutions to the Gross-Pitaevskii equation (GPE) define the topological coherent modes, representing nonground-state Bose-Einstein condensates. These modes can be generated by means of alternating fields whose frequencies are in resonance with the transition frequencies between two collective energy levels corresponding to two different topological modes. The theory of resonant generation of these modes is generalized in several aspects: Multiple-mode formation is described; a shape-conservation criterion is derived, imposing restrictions on the admissible spatial dependence of resonant fields; evolution equations for the case of three coherent modes are investigated; the complete stability analysis is accomplished; the effects of harmonic generation and parametric conversion for the topological coherent modes are predicted. All considerations are realized both by employing approximate analytical methods as well as by numerically solving the GPE. Numerical solutions confirm all conclusions following from analytical methods.