Elastic scattering of a Bose-Einstein condensate at a potential landscape

We investigate the elastic scattering of Bose-Einstein condensates at shallow periodic and disorder potentials. We show that the collective scattering of the macroscopic quantum object couples to internal degrees of freedom of the Bose-Einstein condensate such that the Bose-Einstein condensate gets depleted. As a precursor for the excitation of the Bose-Einstein condensate we observe wave chaos within a mean-field theory.

Wave chaos as signature for depletion of a Bose-Einstein condensate

We study the expansion of repulsively interacting Bose-Einstein condensates (BECs) in shallow one-dimensional potentials. We show for these systems that the onset of wave chaos in the Gross-Pitaevskii equation (GPE), i.e. the onset of exponential separation in Hilbert space of two nearby condensate wave functions, can be used as indication for the onset of depletion of the BEC and the occupation of excited modes within a many-body description. Comparison between the multiconfigurational time-dependent Hartree for bosons (MCTDHB) method and the GPE reveals a close correspondence between the many-body effect of depletion and the mean-field effect of wave chaos for a wide range of single-particle external potentials. In the regime of wave chaos the GPE fails to account for the fine-scale quantum fluctuations because many-body effects beyond the validity of the GPE are non-negligible. Surprisingly, despite the failure of the GPE to account for the depletion, coarse grained expectation values of the single-particle density such as the overall width of the atomic cloud agree very well with the many-body simulations. The time dependent depletion of the condensate could be investigated experimentally, e.g., via decay of coherence of the expanding atom cloud.

Excitation spectra of fragmented condensates by linear response: General theory and application to a condensate in a double-well potential

Linear response of simple (i.e., condensed) Bose-Einstein condensates is known to lead to the Bogoliubov- de Gennes equations. Here, we derive linear response for fragmented Bose-Einstein condensates, i.e., for the case where the many-body wave function is not a product of one, but of several single-particle states (orbitals). Our approach is based on the number-conserving variational time-dependent mean field theory [O. E. Alon, A. I. Streltsov, and L. S. Cederbaum, Phys. Lett. A 362, 453 (2007)], which describes the time evolution of best-mean field states. Correspondingly, we call our linear response theory for fragmented states LR-BMF. In the derivation it follows naturally that excitations are orthogonal to the ground-state orbitals. As applications excitation spectra of Bose-Einstein condensates in double-well potentials are calculated. Both symmetric and asymmetric double-wells are studied for several interaction strengths and barrier heights. The cases of condensed and two-fold fragmented ground states are compared. Interestingly, even in such situations where the response frequencies of the two cases are computed to be close to each other, which is the situation for the excitations well below the barrier, striking differences in the density response in momentum space are found. For excitations with an energy of the order of the barrier height, both the energies and the density response of condensed and fragmented systems are very different. In fragmented systems there is a class of swapped excitations where an atom is transfered to the neighboring well. The mechanism of its origin is discussed. In asymmetric wells, the response of a fragmented system is purely local (i.e., finite in either one or the other well) with different frequencies for the left and right fragments.