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Physical Review A

Stability of Bose-Einstein condensates in two-dimensional optical lattices

Zhu Chen, Biao Wu

Published Apr 13, 2010• 16 citations
Publisher

Abstract

Both Landau instability and dynamical instability of Bose-Einstein condensates in moving two-dimensional optical lattices are investigated numerically and analytically. Phase diagrams for both instabilities are obtained numerically for different system parameters. These phase diagrams show that the Landau instability does not depend on direction for weak lattices while the dynamic instability is direction dependent. These features are explained analytically.

DOI
10.1103/physreva.81.043611

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Both Landau instability and dynamical instability of Bose-Einstein condensates in moving two-dimensional optical lattices are investigated numerically and analytically. Phase diagrams for both instabilities are obtained numerically for different system parameters. These phase diagrams show that the Landau instability does not depend on direction for weak lattices while the dynamic instability is direction dependent. These features are explained analytically.
[[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.
With the help of a set of exact closed-form solutions to the stationary Gross–Pitaevskii equation, we comprehensively investigate Landau and dynamical instabilities of a Bose–Einstein condensate in a periodic array of quantum wells. In the tight-binding limit, the analytical expressions for both Landau and dynamical instabilities are obtained in terms of the compressibility and effective mass of the BEC system. Then the stability phase diagrams are shown to be similar to the one in the case of the sinusoidal optical lattice.
We analyze the dynamical stability of gap solitons formed in a quasi-one-dimensional Bose-Einstein condensate in an optical lattice. Using two different numerical methods we show that, under realistic assumptions for experimental parameters, a gap soliton is stable only in a truly one-dimensional situation. In two and three dimensions, resonant transverse excitations lead to dynamical instability. The time scale of the decay is numerically calculated and shown to be large compared to the characteristic time scale of solitons for realistic physical parameters.
The higher-order interactions of Bose-Einstein condensate in multi-dimensional optical lattices are discussed both analytically and numerically. It is demonstrated that the effects of the higher-order atomic interactions on the sound speed and the stabilities of Bloch waves strongly depend on the lattice strength. In the presence of higher-order effects, tighter and high-dimensional lattices are confirmed to be two positive factors for maintaining the system's energetic stability, and the dynamical instability of Bloch waves can take place simultaneously with the energetic instability. In addition, we find that the higher-order interactions exhibit a long-range behavior and the long-lived coherent Bloch oscillations in a tilted optical lattice exist. Our results provide an effective way to probe the higher-order interactions in optical lattices.