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Chinese Physics Letters

Collective Modes of a Quasi-Two-Dimensional Superfluid Fermi Gas in BCS-BEC Crossover

周昱, 马晓栋, Guoxiang Huang

Published Jan 1, 2006• 0 citations
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Abstract

我们调查集体模式一伪二维(Q2D ) 在 Bardeen-Cooper-Schrieffer Bose 爱因斯坦的超流体费密气体冷凝作用(BCS-BEC ) 转线路。为由使用一个时间家属解决一个概括 Gross-Pitaevskii 方程变化方法，我们与混合 Gaussian 抛物线的类型的形式拿一个试用波浪函数，它不仅反映系统的 Q2D 字符并且也允许这个问题的一条实质上分析的途径。我们在场为各种各样的超流体政体是有效的并且清楚地显示在最大值之间的关系的一个 Q2D 标准压缩了粒子数字和套住潜力以及原子原子相互作用的参数。我们由于在 Q2D 冷凝物的小粒子数字，由量的震荡的频率在强壮的监禁方向迫使的 contribute to 是重要的表演和因此 Thomas 费密近似不能被使用。

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我们调查集体模式一伪二维(Q2D ) 在 Bardeen-Cooper-Schrieffer Bose 爱因斯坦的超流体费密气体冷凝作用(BCS-BEC ) 转线路。为由使用一个时间家属解决一个概括 Gross-Pitaevskii 方程变化方法，我们与混合 Gaussian 抛物线的类型的形式拿一个试用波浪函数，它不仅反映系统的 Q2D 字符并且也允许这个问题的一条实质上分析的途径。我们在场为各种各样的超流体政体是有效的并且清楚地显示在最大值之间的关系的一个 Q2D 标准压缩了粒子数字和套住潜力以及原子原子相互作用的参数。我们由于在 Q2D 冷凝物的小粒子数字，由量的震荡的频率在强壮的监禁方向迫使的 contribute to 是重要的表演和因此 Thomas 费密近似不能被使用。
We investigate the collective modes of a quasi-two-dimensional (Q2D) superfluid Fermi gas in Bardeen–Cooper–Schrieffer Bose–Einstein condensation (BCS-BEC) crossover. For solving a generalized Gross–Pitaevskii equation by using a time-dependent variational method, we take a trial wavefunction with the form of hybrid Gaussian-parabolic type, which not only reflects the Q2D character of the system and also allows an essentially analytical approach of the problem. We present a Q2D criterion that is valid for various superfluid regimes and displays clearly the relation between the maximum condensed particle number and the parameters of trapping potential as well as atom–atom interaction. We show that due to the small particle number in the Q2D condensate, the contribution to oscillating frequencies by the quantum pressure in the strong confinement direction is significant and hence a Thomas–Fermi approximation can not be used.
我们调查通道并且在在到 BoseEinstein 冷凝物(BEC ) 的从 BardeenCooperSchrieffer (英国计算机学会) 超流体的转线路的不同政体的二模式的 ansatz 下面的超流体费密气体自我套住。从状态的一个概括方程开始，我们在一个双井系统关于超流体费密气体导出相对原子对数字和相对阶段的联合方程然后由在原子之间的通道力量和相互作用分类不同摆动行为。通道和自我套住的行为在一个对称的双井潜力的情况中在整个 BCS-BEC 转线路被考虑。我们证明在原子之间的非线性的相互作用做自我套住容易比在 BEC 政体和稳定性分析在英国计算机学会政体认识到的更多也被给。
We investigate collective modes and free expansions of quasi-one- and quasi-two-dimensional (Q1D and Q2D) ultracold Fermi gases in the crossover from a Bardeen-Cooper-Schrieffer (BCS) superfluid to a Bose-Einstein condensate (BEC). We solve a superfluid order parameter equation valid for the BCS-BEC crossover by employing a time-dependent variational method. We take a trial wave function of hybrid Gaussian-parabolic type, which not only reflects the low-dimensional character of the system but also allows an essentially analytical approach for the problem. We present Q1D and Q2D criteria that are valid in various superfluid regimes and show clearly the relation between the maximum condensed particle number and the parameters of the trapping potential as well as the atom-atom interaction. We demonstrate that, due to the small particle number in Q1D and Q2D condensates, the contribution to oscillating frequencies of collective modes by the quantum pressure in the strong-confinement direction is significant and hence the Thomas-Fermi approximation cannot be used. We also show that the free expansion of Q1D and Q2D superfluid Fermi gases in the strong-confinement direction is much faster than that in the weak-confinement direction.
We study the Bogoliubov collective excitations of harmonically trapped superfluid Fermi gases in the crossover from Bardeen-Cooper-Schrieffer (BCS) superfluid to Bose-Einstein condensate (BEC) beyond Thomas-Fermi (TF) limit. Starting from a generalized Gross-Pitaevskii equation and an equation of state valid for the whole crossover, we derive Bogoliubov--de Gennes (BdG) equations for low-lying collective modes at zero temperature. We use a Fetter-like variational ground state wave function to remove the noncontinuity of slope at the boundary of condensate, which appears in the TF limit. We solve the BdG equations analytically and obtain explicit expressions for all eigenvalues and eigenfunctions, valid for various crossover regimes and for traps with spherical and axial symmetries. We discuss the feature of these collective excitations in the BCS-BEC crossover and show that the theoretical result obtained agrees with available experimental data near and beyond the TF limit.