Metastable quantum phase transitions in a periodic one-dimensional Bose gas: Mean-field and Bogoliubov analyses
Metastable quantum phase transitions in a periodic one-dimensional Bose gas: Mean-field and Bogoliubov analyses
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周期性一维玻色气体中的亚稳态量子相变：平均场和 Bogoliubov 分析
DOI：
10.1103/physreva.79.063616
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发表时间：
2009
影响因子：
2.9
通讯作者：
Masahito Ueda
中科院分区：
文献类型：
--
作者：
R. Kanamoto;Lincoln D. Carr;Masahito Ueda
我们推广的概念，量子相变，这是传统上定义的基态，通常适用于在热力学极限，在有限尺寸系统的亚稳态。特别是，我们处理的一维玻色气体的环中存在的相互作用和旋转。为了支持我们的研究，我们带来承担平均场理论，即，非线性薛定谔方程和线性微扰或Bogoliubov\char21{}de Gennes理论。两种方法在弱相互作用下都得到了一致的结果：存在两个拓扑上不同的量子相。第一个是环上玻色-爱因斯坦凝聚体中超流的典型图像：平均角动量是量子化的，超流是均匀的。第二种情况是一个或多个暗孤子以定态出现，打破了对称性，平均角动量变成连续量。因此，冷凝物的相可以连续地缠绕和展开。
We generalize the concept of quantum phase transitions, which is conventionally defined for a ground state and usually applied in the thermodynamic limit, to one for metastable states in finite-size systems. In particular, we treat the one-dimensional Bose gas on a ring in the presence of both interactions and rotation. To support our study, we bring to bear mean-field theory, i.e., the nonlinear Schr\"odinger equation, and linear perturbation or Bogoliubov\char21{}de Gennes theory. Both methods give a consistent result in the weakly interacting regime: there exist two topologically distinct quantum phases. The first is the typical picture of superfluidity in a Bose-Einstein condensate on a ring: average angular momentum is quantized and the superflow is uniform. The second is where one or more dark solitons appear as stationary states, breaking the symmetry, the average angular momentum becomes a continuous quantity. The phase of the condensate can therefore be continuously wound and unwound.