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Chinese Physics Letters

Stability Diagrams of a Bose–Einstein Condensate in a Periodic Array of Quantum Wells

Xue Rui, Liang Zhao-Xin, Weidong Li

Published Jul 1, 2009• 2 citations
Publisher

Abstract

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.

DOI
10.1088/0256-307x/26/7/070303

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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.
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With the help of a set of exact closed-form solutions to the stationary Gross—Pitaevskii (GP) equation, we calculate the collective excitation and quantum depletion of a weakly interacting Bose gas in the presence of a periodic array of quantum wells. The excitation spectrum (Bogoliubov spectrum) is obtained from the solution of the linearized time-dependent GP equation, which develops energy bands ħω j ( p ) periodic in quasi-momentum space. Moreover, we calculate the excitation strengths Z j ( p ) relative to the density operator and then the dynamic structure factor S ( p , ω). Accordingly, the analytical expressions of quantum depletion of the system are obtained. We find that the quantum depletion is enhanced when the interatomic interactions become larger and the potential is sufficiently deep. The conditions for the possible experimental realization of our scenario are also proposed.
We investigate the superfluid properties of a Bose–Einstein condensate (BEC) trapped in a one-dimensional periodic potential. We study, both analytically (in the tight binding limit) and numerically, the Bloch chemical potential, the Bloch energy and the Bogoliubov dispersion relation, and we introduce two different, density dependent, effective masses and group velocities. The Bogoliubov spectrum predicts the existence of sound waves, and the arising of energetic and dynamical instabilities at critical values of the BEC quasi-momentum which dramatically affect its coherence properties. We investigate the dependence of the dipole and Bloch oscillation frequencies in terms of an effective mass averaged over the density of the condensate. We illustrate our results with several animations obtained solving numerically the time-dependent Gross–Pitaevskii equation.
[[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.