Eur. Phys. J. D (2014) 68: 106
https://doi.org/10.1140/epjd/e2014-40835-x

Regular Article

Parametric resonance in Bose-Einstein condensates with periodic modulation of attractive interaction

¹ Institut für Theoretische Physik, Freie Universität Berlin, Arnimallee 14, 14195 Berlin, Germany
² Department of Physics, Queen’s University, Kingston, Ontario, K7L 3N6, Canada
³ JILA, NIST and Department of Physics, University of Colorado, Boulder, CO 80309, USA
⁴ Fachbereich Physik und Forschungszentrum OPTIMAS, Technische Universität Kaiserslautern, 67663 Kaiserslautern, Germany
⁵ Hanse-Wissenschaftskolleg, Lehmkuhlenbusch 4, 27733 Delmenhorst, Germany

^a e-mail: axel.pelster@physik.uni-kl.de

Received: 28 December 2013
Received in final form: 11 February 2014
Published online: 7 May 2014

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.