Vortex lattices in binary Bose-Einstein condensates: Collective modes, quantum fluctuations, and intercomponent entanglement
Vortex lattices in binary Bose-Einstein condensates: Collective modes, quantum fluctuations, and intercomponent entanglement
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二元玻色-爱因斯坦凝聚中的涡晶格：集体模式、量子涨落和组分间纠缠
DOI：
10.1088/1361-6455/ac68b6
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发表时间：
2022
期刊：
影响因子：
--
通讯作者：
Ueda Masahito
中科院分区：
文献类型：
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作者：
Yoshino Takumi;Furukawa Shunsuke;Ueda Masahito
本文研究了在相互平行或反平行方向的合成磁场作用下的二元玻色-爱因斯坦凝聚。在平均场理论中，这两种类型的场被证明给出相同的涡格相图。我们发展了一种改进的有效场理论来研究集体模和基态纠缠的性质。在这里，我们指出需要引入重正化耦合常数的粗粒密度。我们表明，这两种类型的字段的低能激发谱相互关联的重整化耦合常数通过适当的重新标度。通过计算纠缠熵，我们发现，对于一个组件间的排斥（吸引），两个组件更强烈的纠缠在平行（反平行）领域的情况下，在定性协议与最近的研究量子（自旋）霍尔制度。我们还发现，纠缠谱表现出反常的平方根色散关系，这导致了一个subleading对数项的纠缠熵。所有这些都证实了基于Bogoliubov理论与最低朗道能级近似的数值计算。最后，我们通过计算Bogoliubov理论中零点涨落对基态能量的修正，研究了量子涨落对相图的影响。我们发现，菱形，正方形和矩形晶格相之间的边界移动明显的填充因子的减少。
We study binary Bose–Einstein condensates subject to synthetic magnetic fields in mutually parallel or antiparallel directions. Within the mean-field theory, the two types of fields have been shown to give the same vortex-lattice phase diagram. We develop an improved effective field theory to study properties of collective modes and ground-state intercomponent entanglement. Here, we point out the need to introduce renormalized coupling constants for coarse-grained densities. We show that the low-energy excitation spectra for the two types of fields are related to each other by suitable rescaling with the renormalized coupling constants. By calculating the entanglement entropy, we find that for an intercomponent repulsion (attraction), the two components are more strongly entangled in the case of parallel (antiparallel) fields, in qualitative agreement with recent studies for a quantum (spin) Hall regime. We also find that the entanglement spectrum exhibits an anomalous square-root dispersion relation, which leads to a subleading logarithmic term in the entanglement entropy. All of these are confirmed by numerical calculations based on the Bogoliubov theory with the lowest-Landau-level approximation. Finally, we investigate the effects of quantum fluctuations on the phase diagrams by calculating the correction to the ground-state energy due to zero-point fluctuations in the Bogoliubov theory. We find that the boundaries between rhombic-, square-, and rectangular-lattice phases shift appreciably with a decrease in the filling factor.