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arXiv:cond-mat/0611137 · Applied Physics B

Nonexponential decay of Bose–Einstein condensates: a numerical study based on the complex scaling method

Peter Schlagheck, Sandro Wimberger

Published Dec 5, 2006• 33 citations
arXivHTMLPDF
DOI
10.1007/s00340-006-2511-8

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We study the decay dynamics of an interacting Bose-Einstein condensate in the presence of a metastable trap- ping potential from which the condensate can escape via tunnel- ing through finite barriers. The time-dependent decay process is reproduced by means of the instantaneous decay rates of the condensate at a given population of the quasi-bound state, which are calculated with the method of complex scaling. Both for the case of a double-barrier potential as well as for the case of a tilted periodic potential, we find pronounced deviations from a monoexponential decay behavior, which would generally be expected in the absence of the atom-atom interaction.
We have studied the decay of a Bose-Einstein condensate (BEC) of metastable helium atoms in an optical dipole trap. In the regime where two- and three-body losses can be neglected we show that the Bose-Einstein condensate and the thermal cloud show fundamentally different decay characteristics. The total number of atoms decays exponentially with time constant $\ensuremath{\tau}$; however, the thermal cloud decays exponentially with time constant $\frac{4}{3}\ensuremath{\tau}$ and the condensate decays much faster, and nonexponentially. We show that this behavior, which should be present for all BECs in thermal equilibrium with a considerable thermal fraction, is due to a transfer of atoms from the condensate to the thermal cloud during its decay.
The mean-field dynamics of a Bose-Einstein condensate is studied in the presence of a microscopic trapping potential from which the condensate can escape via tunneling through finite barriers. We show that the method of complex scaling can be used to obtain a quantitative description of this decay process. A real-time propagation approach that is applied to the complex-scaled Gross-Pitaevskii equation allows us to calculate the chemical potentials and lifetimes of the metastably trapped Bose-Einstein condensate. The method is applied to a one-dimensional harmonic confinement potential combined with a Gaussian envelope, for which we compute the lowest symmetric and antisymmetric quasibound states of the condensate. A comparison with alternative approaches using absorbing boundary conditions as well as complex absorbing potentials shows good agreement.