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arXiv:0708.2128 · Physical Review A

Self-trapping of Bose-Einstein condensates in optical lattices: The effect of the lattice dimension

Ju-Kui Xue, Ai‐Xia Zhang, Jie Liu

Published Jan 2, 2008• 36 citations
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Abstract

In the present paper, we analytically and numerically investigate the dynamics of Bose-Einstein condensates (BECs) loaded into deep optical lattices of one dimension (1D), 2D, and 3D. We focus on the self-trapped state and the effect of the lattice dimension. Under the tight-binding approximation, we obtain an analytical criterion for the self-trapped state of BEC using the time-dependent variational method. The phase diagram for self-trapping, soliton, breather, or diffusion of a BEC cloud is obtained accordingly and verified by directly solving a discrete Gross-Pitaevskii equation numerically. In particular, we find that the criterion and the phase diagrams are modified dramatically by the dimension of the optical lattices.

DOI
10.1103/physreva.77.013602

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In the present paper, we analytically and numerically investigate the dynamics of Bose-Einstein condensates (BECs) loaded into deep optical lattices of one dimension (1D), 2D, and 3D. We focus on the self-trapped state and the effect of the lattice dimension. Under the tight-binding approximation, we obtain an analytical criterion for the self-trapped state of BEC using the time-dependent variational method. The phase diagram for self-trapping, soliton, breather, or diffusion of a BEC cloud is obtained accordingly and verified by directly solving a discrete Gross-Pitaevskii equation numerically. In particular, we find that the criterion and the phase diagrams are modified dramatically by the dimension of the optical lattices.
The impurity-induced self-trapping and stable moving soliton and breather of two-component Bose-Einstein condensates (BEC's) in deep DDD-dimensional optical lattices are discussed both analytically and numerically. Under the tight-binding approximation and within a time-dependent variational approach, analytical criteria for occurrences of a self-trapping, moving soliton and breather in the system are obtained. The analytical results are confirmed by direct numerical simulation. It is shown that the dynamics of the condensates can be modified significantly by a minor admixture of an impurity (the second component). The diffusion state of the single-component BEC will transit to the self-trapped state due to the minor admixture of an impurity, even if the two condensates are only with marginal spatial overlap. Furthermore, we find that, in certain conditions, a stable moving soliton can exist in high-dimensional lattices for the two-component BEC's, which is very different from the single-component BEC (where a moving soliton cannot be stabilized in high-dimensional lattices). On the other hand, the impurity can play a crucial role in causing important coherence-decoherence and localization-delocalization phase transitions.
We predict the existence of self-trapping, stable, moving solitons and breathers of Fermi wave packets along the Bose-Einstein condensation (BEC)-BCS crossover in one dimension (1D), 2D, and 3D optical lattices. The dynamical phase diagrams for self-trapping, solitons, and breathers of the Fermi matter waves along the BEC-BCS crossover are presented analytically and verified numerically by directly solving a discrete nonlinear Schrödinger equation. We find that the phase diagrams vary greatly along the BEC-BCS crossover; the dynamics of Fermi wave packet are different from that of Bose wave packet.
We study the dynamics of self-trapping in Bose-Einstein condensates (BECs) loaded in deep optical lattices with Gaussian initial conditions, when the dynamics is well described by the discrete nonlinear Schrödinger equation (DNLSE). In the literature an approximate dynamical phase diagram based on a variational approach was introduced to distinguish different dynamical regimes: diffusion, self-trapping, and moving breathers. However, we find that the actual DNLSE dynamics shows a completely different diagram than the variational prediction. We calculate numerically a detailed dynamical phase diagram accurately describing the different dynamical regimes. It exhibits a complex structure that can readily be tested in current experiments in BECs in optical lattices and in optical waveguide arrays. Moreover, we derive an explicit theoretical estimate for the transition to self-trapping in excellent agreement with our numerical findings, which may be a valuable guide as well for future studies on a quantum dynamical phase diagram based on the Bose-Hubbard Hamiltonian.
We develop a five-well model for describing the tunnelling dynamics of Bose-Einstein condensates (BECs) trapped in 2D optical lattices. The tunnelling dynamics of BECs in this five-well model are investigated both analytically and numerically. We focus on the self-trapped states and the difference of the tunnelling dynamics among two-well, three-well and five-well systems. The criterions for the self-trapped states and the phase diagrams of the five trapped BECs in zero-phase mode and π-phase mode are obtained. We find that the criterions and the phase diagrams are largely modified by the dimension of the system and the phase difference between wells. The five-well model is a good model and can give us an insight into the tunnelling dynamics of BECs trapped in 2D optical lattices.
We study the dynamics of a Bose-Einstein condensate wavepacket trapped in an optical lattice. In the tight-binding limit, the system maps onto a discrete nonlinear Schrödinger equation. Using a collective coordinate approximation, we investigate different dynamical regimes: diffusive (in which the boson wavepacket spreads out), self-trapped (with a self-induced pinning), breathing (where the centre of mass of the wavepacket moves with an oscillating width), and solitonic (in which the wavepacket shape is exactly preserved during the dynamics).
The characteristics of two coupled Bose-Einstein Condensate (BEC) bright solitons trapped in an optical lattice are investigated with the variational approach and direct numerical simulations of the Gross-Pitaevskii equation. It is found that the optical lattice can be controllably used to capture and drag the coupled BEC solitons. Its effect depends on the initial location of the BEC solitons, the lattice amplitude and wave-number, and the amplitude of the coupled BEC solitons. The effective interaction between the two coupled solitons is the attractive effect.