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Physical Review Letters

Instability and Depletion of an Excited Bose-Einstein Condensate in a Trap

Yvan Castin, Ralph Dum

Published Nov 10, 1997• 133 citations
Publisher

Abstract

We present an analytical method to calculate the depletion of a Bose-Einstein condensate excited in a time dependent harmonic trap. We identify a regime where the motion of the condensate is unstable and show that this instability leads to an exponentially fast population of noncondensed modes. As these modes are concentrated on the surface of the condensate this is observable in the particle density.

DOI
10.1103/physrevlett.79.3553

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We present an analytical method to calculate the depletion of a Bose-Einstein condensate excited in a time dependent harmonic trap. We identify a regime where the motion of the condensate is unstable and show that this instability leads to an exponentially fast population of noncondensed modes. As these modes are concentrated on the surface of the condensate this is observable in the particle density.
The calculation of properties of Bose-Einstein condensates with dipolar interactions has proven a computationally intensive problem due to the long range nature of the interactions, limiting the scope of applications. In particular, the lowest lying Bogoliubov excitations in three-dimensional harmonic trap with cylindrical symmetry were so far computed in an indirect way, by Fourier analysis of time-dependent perturbations, or by approximate variational methods. We have developed a very fast and accurate numerical algorithm based on the Hankel transform for calculating properties of dipolar Bose-Einstein condensates in cylindrically symmetric traps. As an application, we are able to compute many excitation modes by directly solving the Bogoliubov-De Gennes equations. We explore the behavior of the excited modes in different trap geometries. We use these results to calculate the quantum depletion of the condensate by a combination of a computation of the exact modes and the use of a local density approximation.
We have experimentally studied the unstable dynamics of a harmonically trapped Bose-Einstein condensate loaded into a 1D moving optical lattice. The lifetime of the condensate in such a potential exhibits a dramatic dependence on the quasimomentum state. This is unambiguously attributed to the onset of dynamical instability, after a comparison with the predictions of the Gross-Pitaevskii theory. Deeply in the unstable region we observe the rapid appearance of complex structures in the atomic density profile, as a consequence of the condensate phase uniformity breakdown.
[[abstract]]We study the instabilities, Landau and dynamical instabilities, that are two mechanisms responsible for the breakdown of superfluidity in Bose-Einstein condensates interacting with a one-dimensional optical lattice. An effective-mass Gross-Pitaevskii equation was used to calculate the excitation spectrum and the condensate density of Bose-Einstein condensates in a weak periodic potential. After the condensate velocities greater than the speed of sound, we observe a decreasing of the condensate density, which is the onset of Landau instability. The condensate is dissipated, but not completely, from colliding with the thermal atom cloud. For even higher velocities of the condensate, we find a fast decreasing of the condensate density until full removal of the condensate. The regime of totally removing of the condensate is happened at the inverse effective mass of the condensate becoming zero or negative, where the condensate is on the dynamical instability.