Hannover 2013 – scientific programme
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Q: Fachverband Quantenoptik und Photonik
Q 12: Quantum gases: Bosons I
Q 12.7: Talk
Monday, March 18, 2013, 15:45–16:00, E 001
Parametric resonance in Bose-Einstein condensates — Will Cairncross1 and •Axel Pelster2 — 1Department of Physics, Queen’s University at Kingston, Canada — 2Fachbereich Physik, Technische Universität Kaiserslautern, Germany
We conduct a detailed stability analysis for Bose-Einstein condensates (BECs) in a harmonic trap under parametric excitation by periodic modulation of the s-wave scattering length [1]. To this end we follow Ref. [2] and obtain at first equations of motion for the radial and axial widths of the condensate using a Gaussian variational ansatz for the Gross-Pitaevskii condensate wave function. Linearizing about the equilibrium positions, we obtain a system of coupled Mathieu equations, the stability of which has been studied extensively [3,4]. We carry out an analytic stability analysis for the Mathieu equations, and compare with numerical results for the nonlinear equations of motion. We find qualitative agreement between the Mathieu analytics and the nonlinear numerics, and conclude that the previously unstable (stable) equilibrium of a BEC might be stabilized (destabilized) by parametric excitation.
[1] W. Cairncross and A. Pelster, arXiv:1209.3148
[2] I. Vidanovic, A. Balaz, H. Al-Jibbouri, and A. Pelster, Phys. Rev. A 84, 013618 (2011)
[3] J. Slane and S. Tragesser, Nonl. Dyn. Syst. Th. 11, 183 (2011)
[4] J. Hansen, Arch. Appl. Mech. 55, 463 (1985)