Strongly interacting quantum gases in one-dimensional traps
Strongly interacting quantum gases in one-dimensional traps
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DOI：
10.1103/physreva.91.043634
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发表时间：
2015-02
影响因子：
2.9
通讯作者：
Li Yang;Liming Guan;H. Pu
中科院分区：
文献类型：
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作者：
Li Yang;Liming Guan;H. Pu
在二阶简并微扰理论下，强相互作用区一维囚禁中任意自旋粒子的物理行为可以用超交换相互作用来描述。从这个过程可以构造一个有效的自旋链哈密顿量(非平移不变的萨瑟兰模型)。对于自旋为1/2的粒子，该模型退化为非平移不变的海森堡模型，当相互作用强度从强排斥极限调谐到强吸引极限时，海森堡反铁磁(AFM)和铁磁(FM)态之间有望发生跃迁。我们发现可以用两种不同的方法来区分FM态和AFM态：第一种是基于它们对与自旋相关的磁梯度的不同响应，第二种是基于它们不同的动量分布。通过与几种无偏技术得到的结果进行比较，证实了自旋链模型的有效性
Under the second-order degenerate perturbation theory, we show that the physics of $N$ particles with arbitrary spin confined in a one dimensional trap in the strongly interacting regime can be described by super-exchange interaction. An effective spin-chain Hamiltonian (non-translational-invariant Sutherland model) can be constructed from this procedure. For spin-1/2 particles, this model reduces to the non-translational-invariant Heisenberg model, where a transition between Heisenberg anti-ferromagnetic (AFM) and ferromagnetic (FM) states is expected to occur when the interaction strength is tuned from the strongly repulsive to the strongly attractive limit. We show that the FM and the AFM states can be distinguished in two different methods: the first is based on their distinct response to a spin-dependent magnetic gradient, and the second is based on their distinct momentum distribution. We confirm the validity of the spin-chain model by comparison with results obtained from several unbiased techniques