Parametric Resonance in Bose-Einstein Condensates

TL;DR

This paper investigates how parametric excitation via periodic modulation of the scattering length can induce resonance effects in Bose-Einstein condensates with attractive interactions, affecting their stability.

Contribution

It introduces a nonlinear dynamical model for BEC width oscillations under parametric excitation and analyzes stability changes using both linear and nonlinear methods.

Findings

Parametric resonance can invert BEC stability.

Stability analysis shows qualitative agreement.

Periodic modulation affects condensate widths.

Abstract

We demonstrate parametric resonance in Bose-Einstein condensates (BECs) with attractive two-body interaction in a harmonic trap under parametric excitation by periodic modulation of the s-wave scattering length. We obtain nonlinear equations of motion for the widths of the condensate using a Gaussian variational ansatz for the Gross-Pitaevskii condensate wave function. We conduct both linear and nonlinear stability analyses for the equations of motion and find qualitative agreement, thus concluding that the stability of two equilibrium widths of a BEC might be inverted by parametric excitation.