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Chinese Physics Letters

The Anisotropy of Dipolar Condensate in One-Dimensional Optical Lattices

Lu Tie, Ju-Kui Xue

Published Feb 1, 2012• 1 citation
Publisher

Abstract

The anisotropy of dipole-dipole interaction is revealed by energy band, tunneling dynamics and stabilities of a dipolar condensate in one-dimensional optical lattices. It is demonstrated that the Bloch band structure, the tunneling rate between Bloch bands and the stabilities of Bloch states can be controlled by adjusting the effective aspect ratio of the condensate and the dipolar orientation.

DOI
10.1088/0256-307x/29/2/020301

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The anisotropy of dipole-dipole interaction is revealed by energy band, tunneling dynamics and stabilities of a dipolar condensate in one-dimensional optical lattices. It is demonstrated that the Bloch band structure, the tunneling rate between Bloch bands and the stabilities of Bloch states can be controlled by adjusting the effective aspect ratio of the condensate and the dipolar orientation.
We derive the effective Gross-Pitaevskii equation for a cigar-shaped dipolar Bose-Einstein condensate in one-dimensional lattices and investigate the band structures numerically. Due to the anisotropic and the long-ranged dipole-dipole interaction in addition to the known contact interaction, we elucidate the possibility of modifying the band structures by changing the alignment of the dipoles with the axial direction. With the considerations of the transverse parts and the practical physical parameters of a cigar-shaped trap, we show the possibility to stabilize an attractive condensate simply by adjusting the orientation angle of dipoles. Some interesting Bloch waves at several particle current densities are identified for possible experimental observations.
The energy band structure of spin-1 condensates with repulsive spin-independent and either ferromagnetic or antiferromagnetic spin-dependent interactions in one-dimensional (1D) periodic optical lattices is discussed. Within the two-mode approximation, Bloch bands of spin-1 condensates are presented. The results show that the Bloch bands exhibit a complex structure as the atom density of mF = 0 hyperfine state increases: bands splitting, reversion, intersection and loop structure are excited subsequently. The complex band structure should be related to the tunneling and spin-mixing dynamics.
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 report experimental results on the properties of Bose-Einstein condensates in one-dimensional optical lattices. By accelerating the lattice, we observed Bloch oscillations of the condensate in the lowest band, as well as Landau-Zener (LZ) tunneling into higher bands when the lattice depth was reduced and/or the acceleration of the lattice was increased. The dependence of the LZ tunneling rate on the condensate density was then related to mean-field effects modifying the effective potential acting on the condensate, yielding good agreement with recent theoretical work. We also present several methods for measuring the lattice depth and discuss the effects of the micromotion in the time-orbiting-potential trap on our experimental results.
Motivated by the recent experimental achievements in using the Bragg spectroscopy to measure the excitation spectrum of an ultra-cold atomic system with long-range interactions, we investigate the dynamic structure factor of a cigar-shaped dipolar Bose condensate trapped in a one-dimensional optical lattices. Our results show that the Bogoliubov bands of the system, particularly the lowest one, can be significantly influenced when one tunes the dipole orientation. Consequently, the calculated static structure factor of an optically trapped dipolar Bose gas shows marked difference from the non-dipolar one. Moreover, we show that the effects of dipole-dipole interaction on the dynamic structure factor is also strongly affected by the strength of the optical confinement.
Solitons of dipolar spinor condensates confined in a one-dimensional optical lattice are studied in terms of the equation of motion of the spinor which is reduced to the sine-Gordon equation in the limit of strong dipole–dipole interaction and weak external magnetic field. It is shown that the solitons obtained analytically can be easily controlled by adjusting the light-induced dipolar interaction, which is realizable in the optical lattice created by red-detuned laser beams with modulating intensity. The possible creation and detection schemes are also proposed.