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Chinese Physics Letters

Stability Diagrams of a Bose–Einstein Condensate in Excited Bloch Bands

Liang Zhao-Xin, Hu Ban-Bi

Published Jan 1, 2009• 2 citations
Publisher

Abstract

Landau and dynamical instabilities of a Bose–Einstein condensate (BEC) in the excited bands of a one-dimensional optical lattice are investigated by the Gross–Pitaevskii theory. Our results show that there always exists Landau instability for a BEC in the whole region of excited bands. We also map out the dangerous zones of the dynamical instability. The experimental implications of the stability diagram are discussed.

DOI
10.1088/0256-307x/26/1/016701

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Landau and dynamical instabilities of a Bose–Einstein condensate (BEC) in the excited bands of a one-dimensional optical lattice are investigated by the Gross–Pitaevskii theory. Our results show that there always exists Landau instability for a BEC in the whole region of excited bands. We also map out the dangerous zones of the dynamical instability. The experimental implications of the stability diagram are discussed.
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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.
Energy band structure and stability of Bose-Einstein condensate with both two- and three-body interactions in one-dimensional periodic optical lattices are discussed. It is demonstrated that the lowest energy band can show a loop structure at the boundary of the first Brillouin zone only when the number of atoms is larger than a critical value. When the loop structure is excited, an analytical expression of the loop width is obtained. The energetical and dynamical stabilities of the system are determined by considering the behavior of the Gross-Pitaevskii energy functional when the condensate wave function diverge away from a stationary state upon small perturbation, and its dependence on the number of atoms, the magnitude of the periodic potential, especially, the strength of the three-body force are studied. In addition, a criteria of the stability for excitations with long wavelengths is given by applying the hydrodynamic approach. The influence of the three-body interaction on the band properties and the stabilities are discussed in detail. It is shown that the critical density for developing the loop structure, the loop width, and the instability criteria are modified dramatically by the three-body interaction.
We investigate the band structure of a Bose-Einstein condensate in a one-dimensional periodic potential by calculating stationary solutions of the Gross-Pitaevskii equation, which have the form of Bloch waves. We demonstrate that loops (``swallow tails'') in the band structure occur both at the Brillouin zone boundary and at the center of the zone, and they are therefore a generic feature. A physical interpretation of the swallow tails in terms of periodic solitons is given. The linear stability of the solutions is investigated as a function of the strength of the mean-field interaction, the magnitude of the periodic potential, and the wave vector of the condensate. The regions of energetic and dynamical stability are identified by considering the behavior of the Gross-Pitaevskii energy functional for small deviations of the condensate wave function from a stationary state. It is also shown how for long-wavelength disturbances the stability criteria may be obtained within a hydrodynamic approach.