无限光晶格中排斥束缚原子对的动力学和对称性
Dynamics and symmetries of a repulsively bound atom pair in an infinite optical lattice
摘要：
在玻色-哈伯德模型的框架下，研究了一维无限光晶格势场中两玻色子的动力学行为，得到了有限时刻波函数的精确表达式.作为初始条件，我们选择了本地化的原子，由$d$晶格位置的距离分开，并携带一个质心准动量。当相互作用和/或质量质心准动量增加时，发现初始局部化对（$d=0$）更稳定，如通过对概率（在相同晶格位置找到两个原子的概率）量化的。对于初始分离的原子（$d \neq 0$），存在一个最佳的相互作用强度。在无限时间的限制下，计算了波函数、对几率和对形成的最佳相互作用强度的简单表达式。与时间相关的波函数对于相互作用强度的值的不同仅在于符号，而重要的可观测量如密度和对概率则没有。对称性分析表明，这种行为扩展到$N$粒子水平和费米子系统。我们的结果提供了一个补充的理解最近观察到的[温克勒\textit{et al.}，自然（伦敦）\textbf{441}，853（2006）]动力学稳定性的原子对在排斥相互作用格子气。
英文摘要：
We investigate the dynamics of two bosons trapped in an infinite one-dimensional optical lattice potential within the framework of the Bose-Hubbard model and derive an exact expression for the wavefunction at finite time. As initial condition we chose localized atoms that are separated by a distance of $d$ lattice sites and carry a center of mass quasi-momentum. An initially localized pair ($d=0$) is found to be more stable as quantified by the pair probability (probability to find two atoms at the same lattice site) when the interaction and/or the center of mass quasi-momentum is increased. For initially separated atoms ($d \neq 0$) there exists an optimal interaction strength for pair formation. Simple expressions for the wavefunction, the pair probability and the optimal interaction strength for pair formation are computed in the limit of infinite time. Whereas the time-dependent wavefunction differs for values of the interaction strength that differ only by the sign, important observables like the density and the pair probability do not. With a symmetry analysis this behavior is shown to extend to the $N$-particle level and to fermionic systems. Our results provide a complementary understanding of the recently observed [Winkler \textit{et al.}, Nature (London) \textbf{441}, 853 (2006)] dynamical stability of atom pairs in a repulsively interacting lattice gas.
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