论文标题
超速原子与一组固定杂质相互作用的绑定状态
Bound states of an ultracold atom interacting with a set of stationary impurities
论文作者
论文摘要
在本手稿中，我们分析了与一组静态杂质相互作用的原子的结合状态的性质。我们从与两个静态杂质相互作用的单个原子的最简单系统开始。我们考虑了两种类型的原子 - 障碍相互作用：（i）由正规化三角洲表示的零范围势，（ii）更逼真的极化电位，代表了原子 - 离子相互作用的远距离部分。对于前者，我们获得了结合状态能量的分析结果。对于后者，我们根据有限元方法的应用执行数值计算。然后，我们转移到与一维无限链静态离子相互作用的单个原子的情况下。这样的设置类似于1D晶体固体的Kronig-Penney模型，其中能量谱显示带状结构的行为。对于该系统，我们为假定正规化的三角洲相互作用的结合状态的带结构得出分析结果，并执行数值计算，考虑到极化潜力来模拟原子不良性相互作用。当杂质之间的分离远大于相互作用潜力的特征范围时，两种方法都很好。
In this manuscript we analyse properties of bound states of an atom interacting with a set of static impurities. We begin with the simplest system of a single atom interacting with two static impurities. We consider two types of atom-impurity interaction: (i) zero-range potential represented by regularized delta, (ii) more realistic polarization potential, representing long-range part of the atom-ion interaction. For the former we obtain analytical results for energies of bound states. For the latter we perform numerical calculations based on the application of finite element method. Then, we move to the case of a single atom interacting with one-dimensional (1D) infinite chain of static ions. Such a setup resembles Kronig-Penney model of a 1D crystalline solid, where energy spectrum exhibits band structure behaviour. For this system, we derive analytical results for the band structure of bound states assuming regularized delta interaction, and perform numerical calculations, considering polarization potential to model atom-impurity interaction. Both approaches agree quite well when separation between impurities is much larger than characteristic range of the interaction potential.
