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Communications in Theoretical Physics

Bose—Einstein Condensates in Optical Lattices with Higher-Order Interactions

Ai‐Xia Zhang, Ju-Kui Xue

Published Apr 1, 2012• 1 citation
Publisher

Abstract

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.

DOI
10.1088/0253-6102/57/4/13

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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.
The nonlinear Landau—Zener tunneling and nonlinear Rabi oscillations of Bose—Einstein condensate (BEC) with higher-order atomic interaction between the Bloch bands in an accelerating optical lattice are discussed. Within the two-level model, the tunneling probability of BEC with higher-order atomic interaction between Bloch bands is obtained. We finds that the tunneling rate is closely related to the higher-order atomic interaction. Furthermore, the nonlinear Rabi oscillations of BEC with higher-order atomic interaction between the bands are discussed by imposing a periodic modulation on the level bias. Analytical expressions of the critical higher-order atomic interaction for suppressing/enhancing the Rabi oscillations are obtained. It is shown that the critical value strongly depends on the modulation parameters (i.e., the modulation amplitude and frequency) and the strength of periodic potential.
Superflow of a Bose–Einstein condensate in an optical lattice is represented by a Bloch wave, a plane wave with periodic modulation of the amplitude. We review the theoretical results of the interaction effects in the energy dispersion of the Bloch waves and in the linear stability of such waves. For sufficiently strong repulsion between the atoms, the lowest Bloch band develops a loop at the edge of the Brillouin zone, with the dramatic consequence of a finite probability of Landau–Zener tunnelling even in the limit of a vanishing external force. Superfluidity can exist in the central region of the Brillouin zone in the presence of a repulsive interaction, beyond which Landau instability takes place where the system can lower its energy by making a transition into states with smaller Bloch wavenumbers. In the outer part of the region of Landau instability, the Bloch waves are also dynamically unstable in the sense that a small initial deviation grows exponentially in time. In the inner region of Landau instability, a Bloch wave is dynamically stable in the absence of persistent external perturbations. Experimental implications of our findings will be discussed.
The speed of sound of a Bose-Einstein condensate in an optical lattice is studied both analytically and numerically in all spatial three dimensions. Our investigation shows that the sound speed depends strongly on the strength of the lattice. In the one-dimensional case, the speed of sound falls monotonically with increasing lattice strength. The dependence on lattice strength becomes much richer in two and three dimensions. In the two-dimensional case, when the interaction is weak, the sound speed first increases and then decreases as the lattice strength increases. For the three-dimensional lattice, the sound speed can even oscillate with the lattice strength. These rich behaviors can be understood in terms of compressibility and effective mass. Our analytical results in the limit of weak lattices also offer an interesting perspective to help with our understanding: they show that the lattice component perpendicular to the sound propagation increases the sound speed while the lattice component parallel to the propagation decreases the sound speed. The various dependences of the sound speed on the lattice strength are the result of this competition.
We study the dynamics of Bose-Einstein condensates in tilted and driven optical superlattices. For a bichromatic lattice, each Bloch band splits up into two minibands such that the dynamics is governed by the interplay of Bloch oscillations and transitions between the bands. Thus, bichromatic potentials provide an excellent model system for the study of nonlinear Landau-Zener tunneling, and they allow for a variety of applications in matter-wave interferometry and quantum metrology. In the present paper, we investigate the coherent dynamics of an interacting Bose-Einstein condensate as well as its stability. Different mechanisms of instability are discussed, which lead to a rapid depletion of the condensate.
We study dynamical and energetic instabilities in the transport properties of Bloch waves for atomic multicomponent Bose-Einstein condensates in optical lattices in the tight-binding limit. We obtain stability criteria analytically, as a function of superfluid velocities and interaction parameters, in several cases, for two-component and spinor condensates. In the two-species case we find that the presence of the other condensate component can stabilize the superfluid flow of an otherwise unstable condensate and that the free space dynamical miscibility condition of the two species can be reversed by tuning the superfluid flow velocities. In spin-1 condensates, we find the steady-state Bloch wave solutions and characterize their stability criteria. We find that generally more regions of dynamical instability arise for the polar than for the ferromagnetic solutions. In the presence of magnetic Zeeman shifts, we find a richer variety of condensate solutions and find that the linear Zeeman shift can stabilize the superfluid flow in several cases of interest.
We present the results of experimental work on the dynamics of a Bose-Einstein condensate (BEC) loaded in a 1D moving optical lattice. The system is studied both in the regime of low atomic density (expanding BEC) and high atomic density (trapped BEC). In the low-density regime, the stable dynamics of the system is well-described in terms of Bloch waves. In the presence of nonlinearities, as in a high-density sample, the Bloch waves are not stable solutions of the Gross-Pitaevskii equation (GPE) and dynamical instability takes place.