Exact results for persistent currents of two bosons in a ring lattice
Exact results for persistent currents of two bosons in a ring lattice
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环形晶格中两个玻色子持续电流的精确结果
作者：
J. Polo;P. Naldesi;A. Minguzzi;L. Amico
研究了两个相互作用玻色子在合成磁通作用下的基态。该系统由玻色-哈伯德模型描述，并通过波函数的平面波近似精确求解。我们得到的排斥和吸引相互作用的系统的能量和相关函数。与Lieb-Liniger模型描述的一维连续理论不同，在格点情形下，我们证明了两个粒子的质心与其相对坐标是耦合的。在制度的持续流动中，鲜明的特征清晰地显现出来。而对于排斥玻色子的持续电流显示的周期性所给出的任何相互作用强度的标准通量量子，在吸引力的情况下，通量量子成为分馏的方式，取决于相互作用。我们还研究了系统长时间膨胀后的密度，这为在冷原子环境中探测持续电流提供了一条实验可行的途径。我们的结果可用于基准的多体问题的近似方案。
We study the ground state of two interacting bosonic particles confined in a ring-shaped lattice potential and subjected to a synthetic magnetic flux. The system is described by the Bose-Hubbard model and solved exactly through a plane-wave Ansatz of the wave function. We obtain energies and correlation functions of the system both for repulsive and attractive interactions. In contrast with the one-dimensional continuous theory described by the Lieb-Liniger model, in the lattice case we prove that the center of mass of the two particles is coupled with its relative coordinate. Distinctive features clearly emerge in the persistent current of the system. While for repulsive bosons the persistent current displays a periodicity given by the standard flux quantum for any interaction strength, in the attractive case the flux quantum becomes fractionalized in a manner that depends on the interaction. We also study the density after the long time expansion of the system which provides an experimentally accessible route to detect persistent currents in cold atom settings. Our results can be used to benchmark approximate schemes for the many-body problem.