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Journal of Physics Conference Series

Dynamical instability of a two component Bose-Einstein Condensate in an optical lattice

Mehmet Emre Taşgın, Mehmet Özgür Oktel

Published Apr 1, 2006• 1 citation
Publisher

Abstract

We investigate the dynamical instability for a two component Bose-Einstein Condensate (BEC) in an optical lattice. We assume that the two components are in sinusoidal potentials with the same period but different phases. We find a swallow-tail type instability near the band edge, however an extra tail is formed due to the inter-component interaction. Depending on the phase difference of the potentials, the instability region may expand or shrink with increasing inter-component interaction.

DOI
10.1088/1742-6596/36/1/030

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We investigate the dynamical instability for a two component Bose-Einstein Condensate (BEC) in an optical lattice. We assume that the two components are in sinusoidal potentials with the same period but different phases. We find a swallow-tail type instability near the band edge, however an extra tail is formed due to the inter-component interaction. Depending on the phase difference of the potentials, the instability region may expand or shrink with increasing inter-component interaction.
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The stability of the ground state of two-component Bose–Einstein condensates (BECs) loaded into the central well of an axially symmetric Bessel lattices (BLs) potential with attractive or repulsive atoms interactions is studied using the time-dependent Gross–Pitaevskii equation (GPE). By using the variational method, we find that stable ground state of two-component BECs can exist in BLs. The BLs's depth and the intra-species atom interaction play an important role in the stability of ground state. The collapse of two-component BECs in BLs is also studied and a collapse condition for trapped two-component BECs is obtained. It is shown that the two-component BECs exhibit rich collapse dynamics. That is, the two-component BECs can collapse in the system with both intra- and inter-attractive, or with intra-attractive and inter-repulsive, or with intra-repulsive and inter-attractive atom interactions. Furthermore, the control of the collapse of the two-component BECs in BLs is discussed in detail. The stability diagram of the ground state in parameter space is obtained. The results show that the collapse of two-component BECs can be controlled by temporal modulation of the atom interaction.
We study modulational instability of two-component Bose-Einstein condensates in an optical lattice, which is modeled as a coupled discrete nonlinear Schr\"odinger (DNLS) equation. The excitation spectrum and the modulational instability condition of the total system are presented analytically. In the long-wavelength limit, our results agree with the homogeneous two-component Bose-Einstein condensates case. The discreteness effects result in the appearance of the modulational instability for the condensates in miscible region. The numerical calculations confirm our analytical results and show that the interspecies coupling can transfer the instability from one component to another.