arXiv 1208.07342012-08cond-mat.quant-gas

环形玻色-爱因斯坦凝聚体流过势垒的临界速度

Critical velocity for a toroidal Bose-Einstein condensate flowing through a barrier

Francesco Piazza, Lee A. Collins, Augusto Smerzi

备注：: Extended version
发表信息：: J. Phys. B: At. Mol. Opt. Phys. 46 (2013) 095302
DOI：: 10.1088/0953-4075/46/9/095302

摘要：

我们考虑在最近的实验中采用的设置（Ramanathan等人2011 Phys. Rev. Lett. 106 130401）致力于研究在存在排斥性光学势垒的情况下环形玻色-爱因斯坦凝聚体的超流流动的不稳定性。使用Gross-Pitaevskii平均场方程，我们观察到，与我们在Piazza et al（2009 Phys. Rev. A 80 021601）中发现的一致，具有一个单位角动量的超流在临界强度的屏障处变得不稳定，并通过由涡旋-反涡旋线对湮灭执行的相位滑移机制衰减。虽然该图在定性上与实验结果一致，但Gross-Pitaevskii方程不能很好地再现测量的临界势垒高度，表明热波动可能起重要作用（Mathey等人，2012 arXiv：1207.0501）。作为另一种解释的差异，我们认为成像系统的有限分辨率的影响。在临界点处，障碍物附近的超流速度总是在该区域的声速$v_{\rm barr}=c_{\rm l}$的数量级。特别是，在流体动力学制度（在上述实验中没有达到），临界点是通过应用朗道标准内的障碍区。另一方面，Feynman临界速度$v_{\rm f}$远低于观测到的临界速度。我们认为，这是一个一般特征的Gross-Pitaevskii方程，我们有$v_{\rm f}=ε c_{\rm l}$与$ε$是一个小参数的模型。考虑到这些观测结果，关于超流体不稳定性的本质的问题仍然没有解决。

英文摘要：

We consider the setup employed in a recent experiment (Ramanathan et al 2011 Phys. Rev. Lett. 106 130401) devoted to the study of the instability of the superfluid flow of a toroidal Bose-Einstein condensate in presence of a repulsive optical barrier. Using the Gross-Pitaevskii mean-field equation, we observe, consistently with what we found in Piazza et al (2009 Phys. Rev. A 80 021601), that the superflow with one unit of angular momentum becomes unstable at a critical strength of the barrier, and decays through the mechanism of phase slippage performed by pairs of vortex-antivortex lines annihilating. While this picture qualitatively agrees with the experimental findings, the measured critical barrier height is not very well reproduced by the Gross-Pitaevskii equation, indicating that thermal fluctuations can play an important role (Mathey et al 2012 arXiv:1207.0501). As an alternative explanation of the discrepancy, we consider the effect of the finite resolution of the imaging system. At the critical point, the superfluid velocity in the vicinity of the obstacle is always of the order of the sound speed in that region, $v_{\rm barr}=c_{\rm l}$. In particular, in the hydrodynamic regime (not reached in the above experiment), the critical point is determined by applying the Landau criterion inside the barrier region. On the other hand, the Feynman critical velocity $v_{\rm f}$ is much lower than the observed critical velocity. We argue that this is a general feature of the Gross-Pitaevskii equation, where we have $v_{\rm f}=ε c_{\rm l}$ with $ε$ being a small parameter of the model. Given these observations, the question still remains open about the nature of the superfluid instability.

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