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arXiv:1108.1857 · Physical Review A

Vortex formation of a Bose-Einstein condensate in a rotating deep optical lattice

Akira Kato, Yuki Nakano, Kenichi Kasamatsu, Tetsuo Matsui

Published Nov 18, 2011• 26 citations
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Abstract

We study the dynamics of vortex nucleation and lattice formation in a Bose--Einstein condensate in a rotating square optical lattice by numerical simulations of the Gross--Pitaevskii equation. Different dynamical regimes of vortex nucleation are found, depending on the depth and period of the optical lattice. We make an extensive comparison with the experiments by R. A. Williams et al. [Phys. Rev. Lett. 104, 050404 (2010)], especially focusing on the issues of the critical rotation frequency for the first vortex nucleation and the vortex number as a function of rotation frequency.

DOI
10.1103/physreva.84.053623

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We report the observation of vortex nucleation in a rotating optical lattice. A 87Rb Bose-Einstein condensate was loaded into a static two-dimensional lattice and the rotation frequency of the lattice was then increased from zero. We studied how vortex nucleation depended on optical lattice depth and rotation frequency. For deep lattices above the chemical potential of the condensate we observed a linear dependence of the number of vortices created with the rotation frequency, even below the thermodynamic critical frequency required for vortex nucleation. At these lattice depths the system formed an array of Josephson-coupled condensates. The effective magnetic field produced by rotation introduced characteristic relative phases between neighboring condensates, such that vortices were observed upon ramping down the lattice depth and recombining the condensates.
We numerically study the dynamics of vortex lattice formation in a rotating cigar-shaped Bose-Einstein condensate. The study is a three-dimensional simulation of the Gross-Pitaevskii equation with a phenomenological dissipation term. The simulations reveal previously unknown dynamical features of the vortex nucleation process, in which the condensate undergoes a strongly turbulent stage and the penetrating vortex lines vibrate rapidly. The vibrations arise from spontaneous excitation of Kelvin waves on the protovortices during a surface wave instability, caused by an inhomogeneity of the condensate density along the elongated axial direction.
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In this paper, we study the static and dynamic properties of vortices formation in a rotating Bose–Einstein condensate in synthetic magnetic field. The condensate is confined in a harmonic potential and an optical lattice potential. We numerically solve the time-dependent Gross–Pitaevskii equation in two dimensions and compare the vortices formation process with rotating frame method. We derive the two expressions about vortex number N[Formula: see text] and chemical potential [Formula: see text] as a function of rotational frequency [Formula: see text], which show that the number of vortices N[Formula: see text] increases linearly with [Formula: see text], while the chemical potential [Formula: see text] remains nearly unchanged with increasing [Formula: see text]. The analytical results are in qualitative agreement with the numerical ones. Moreover, we also investigate the vortex dynamics. Numerical results indicate that the time spent for the formation of steady state vortices is reduced drastically if the optical lattice is considered. Nevertheless, the synthetic magnetic field approach is still low efficient to generate more vortices.