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Physical Review A

Coherent matter waves of a dipolar condensate in two-dimensional optical lattices

Ai‐Xia Zhang, Ju-Kui Xue

Published Jul 8, 2010• 23 citations
Publisher

Abstract

The coherent matter waves of a dipolar condensate in deep two-dimensional (2D) tilted and nontilted optical lattices are studied both analytically and numerically. It is shown that, in tilted lattices, by properly designing the sign and the magnitude of the contact interaction and the dipolar interaction, it is possible to control the decoherence of Bloch oscillations. Contrary to the usual short-range interacting Bose system, long-lived Bloch oscillations of the dipolar condensate are achieved when the dipolar interaction, the contact interaction, and the lattice dimension satisfy an analytical condition. Furthermore, we predict that, in untilted lattices, stable coherent 2D moving soliton and breather states of the dipolar condensate exist. This fact is very different from the purely short-range interacting Bose system (where the moving soliton cannot be stabilized in high-dimensional lattices). The dipolar interaction can lead to some novel phenomena that can not appear in short-range interacting BEC system.

DOI
10.1103/physreva.82.013606

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The coherent matter waves of a dipolar condensate in deep two-dimensional (2D) tilted and nontilted optical lattices are studied both analytically and numerically. It is shown that, in tilted lattices, by properly designing the sign and the magnitude of the contact interaction and the dipolar interaction, it is possible to control the decoherence of Bloch oscillations. Contrary to the usual short-range interacting Bose system, long-lived Bloch oscillations of the dipolar condensate are achieved when the dipolar interaction, the contact interaction, and the lattice dimension satisfy an analytical condition. Furthermore, we predict that, in untilted lattices, stable coherent 2D moving soliton and breather states of the dipolar condensate exist. This fact is very different from the purely short-range interacting Bose system (where the moving soliton cannot be stabilized in high-dimensional lattices). The dipolar interaction can lead to some novel phenomena that can not appear in short-range interacting BEC system.
Within the mean-field model, the coherent matter waves of a dipolar condensate in a harmonic potential superimposed to a deep lattice are investigated by the variational principle. It is shown that, in a harmonic potential superimposed to a deep lattice, it is possible to control the decoherence of Bloch oscillations due to the fact that the on-site and the inter-site dipolar interactions can not only damp out Bloch oscillations but also maintain long-lived Bloch oscillations under the certain condition. In particular, long-lived Bloch oscillations of dipolar condensate can be realized when the dipolar interaction, the contact interaction, the frequency of the harmonic potential and initial width of the wave packet satisfy an analytical condition. Thus the decoherence of Bloch oscillation can be controlled by adjusting the dipolar interaction, the contact interaction, the frequency of harmonic potential and the initial width of the wave packet.
We study the stabilization properties of dipolar Bose–Einstein condensate in a deep one-dimensional optical lattice with an additional external parametrically modulated harmonic trap potential. Through both analytical and numerical methods, we solve a dimensionless nonlocal nonlinear discrete Gross–Pitaevskii equation with both the short-range contact interaction and the long-range dipole–dipole interaction. It is shown that, the stability of dipolar condensate in modulated deep optical lattice can be controled by coupled effects of the contact interaction, the dipolar interaction and the external modulation. The system can be stabilized when the dipolar interaction, the contact interaction, the average strength of potential and the ratio of amplitude to frequency of the modulation satisfy a critical condition. In addition, the breather state, the diffused state and the attractive-interaction-induced-trapped state are predicted. The dipolar interaction and the external modulation of the lattice play important roles in stabilizing the condensate.
We analyze the physics of bright solitons in 2D dipolar Bose-Einstein condensates. These solitons, which are not possible in short-range interacting gases, constitute the first realistic proposal of fully mobile stable 2D solitons in ultracold gases. In particular, we discuss the necessary conditions for the existence of stable 2D bright solitary waves by means of a 3D analysis of the lowest-lying excitations. We show that the anisotropy of the dipolar potential is crucial, since sufficiently large dipolar interactions can destabilize the 2D soliton. Additionally, we study the scattering of solitary waves, which, contrary to the contact-interacting case, is inelastic and could lead to fusion of the waves. Finally, the experimental possibilities for observability are discussed.
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 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.
Atomic interaction leads to dephasing and damping of Bloch oscillations (BOs) in optical lattices, which limits observation and applications of BOs. How to obtain persistent BOs is particularly important. Here, the nonlinear Bloch dynamics of the Bose–Einstein condensate with two-body and three-body interactions in deep optical lattices is studied. The damping rate induced by interactions is obtained. The damping induced by two-body interaction plays a dominant role, while the damping induced by three-body interaction is weak. However, when the two-body and three-body interactions satisfy a threshold, long-lived coherent BOs are observed. Furthermore, the Bloch dynamics with periodical modulation of linear force is studied. The frequencies of linear force corresponding to resonance and pseudoresonance are obtained, and rich dynamical phenomena, i.e., stable and strong BOs, drifting and dispersion of wave packet, are predicted. The controllable Bloch dynamics is provided with the periodic modulation of the linear force.