周期性驱动的玻色-爱因斯坦凝聚体对的 Fock 空间中的规范势与涡旋
Gauge potentials and vortices in the Fock space of a pair of periodically driven Bose-Einstein condensates
AI总结：
本文研究了周期性驱动双势阱中两物种玻色-爱因斯坦凝聚体的耦合动力学，利用 Floquet 分析推导出含人工规范场的有效哈密顿量，发现种内吸引相互作用达临界值时基态在 Fock 空间发生从高斯态到量子化涡旋态的转变。
摘要：
我们对双势阱中两种玻色-爱因斯坦凝聚体（BEC）的耦合动力学进行了理论研究，其中隧穿和原子间相互作用均随时间周期性驱动。每种物质在势阱间的布居数差在 Fock 空间中形成了一个二维晶格，其维度由每个 BEC 的原子数决定。我们使用 Floquet 分析推导出作用于该 Fock 空间的有效哈密顿量，并发现其中包含人工规范场。该系统模拟了紧束缚晶格中受附加谐振势和矢量势影响的非相互作用粒子。当种内相互作用为吸引性时，存在一个临界值，在该值处 Floquet 算符的基态在 Fock 空间中经历从高斯态到量子化涡旋态的转变。该转变可通过角动量及基态的纠缠熵来量化，随着种内相互作用增强，两者均表现出突然跃变。在热力学极限下，涡旋态的稳定性消失。
英文摘要：
We perform a theoretical study of the coupled dynamics of two species of Bose-Einstein condensates (BECs) in a double well potential where both the tunneling and the interatomic interactions are driven periodically in time. The population difference between the wells of each species gives rise to a two dimensional lattice in Fock space with dimensions given by the number of atoms in each BEC. We use a Floquet analysis to derive an effective Hamiltonian that acts in this Fock space and find that it contains an artificial gauge field. This system simulates noninteracting particles in a tight binding lattice subject to an additional harmonic potential and vector potential. When the intra-species interactions are attractive there is a critical value at which the ground state of the Floquet operator undergoes a transition from a Gaussian state to a quantized vortex state in Fock space. The transition can be quantified in terms of the angular momentum as well as the entanglement entropy of the ground state with both showing sudden jumps as the intra-species interactions become stronger. The stability of the vortex state vanishes in the thermodynamic limit.
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