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Dynamics and stability of Bose-Einstein condensates with attractive 1r interaction.pdf

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Dynamics and stability of Bose-Einstein condensates with attractive 1r interaction

a r X i v : 0 8 0 3 .1 7 9 9 v 2 [ q u a n t - p h ] 2 9 A p r 2 0 0 8 Dynamics and stability of Bose-Einstein condensates with attractive 1/r interaction Holger Cartarius,? Tomaz? Fabc?ic?, Jo?rg Main, and Gu?nter Wunner Institut fu?r Theoretische Physik 1, Universita?t Stuttgart, 70550 Stuttgart, Germany (Dated: April 29, 2008) The time-dependent extended Gross-Pitaevskii equation for Bose-Einstein condensates with at- tractive 1/r interaction is investigated with both a variational approach and numerically exact calculations. We show that these condensates exhibit signatures known from the nonlinear dy- namics of autonomous Hamiltonian systems. The two stationary solutions created in a tangent bifurcation at a critical value of the scattering length are identified as elliptical and hyperbolical fixed points, corresponding to stable and unstable stationary states of the condensate. The stable stationary state is surrounded by elliptical islands, corresponding to condensates periodically oscil- lating in time, whereas condensate wave functions in the unstable region undergo a collapse within finite time. For negative scattering lengths below the tangent bifurcation no stationary solutions exist, i.e., the condensate is always unstable and collapses. PACS numbers: 03.75.Kk, 34.20.Cf, 04.40.-b, 05.45.-a I. INTRODUCTION Bose condensates with atomic interactions, in addition to the contact interaction, open the possibility to study the properties of degenerate quantum gases in which the relative strengths of long- and short-range interactions can be continuously adjusted by tuning the contact inter- action via a Feshbach resonance. In particular, the Bose- Einstein condensation of neutral atoms with electromag- netically induced attractive 1/r interaction has been pro- posed. According to O’Dell et al. [1] “monopolar” quan- tum gases could be realized by a combination of 6 appro- priately arranged “triads” of intense off-resonant laser beams. In that arrangemen