光学超晶格中的磁性、相干多粒子动力学和超冷玻色子弛豫
Magnetism, coherent many-particle dynamics, and relaxation with ultracold bosons in optical superlattices
摘要：
我们研究如何以及磁模型可以实现两个不同的超精细态的超冷玻色子原子的光学超晶格。该系统是由两种玻色-哈伯德模型捕获的，但在一定的参数范围内，实际上实现了自旋为1/2的海森堡磁体的物理，描述了二阶跳跃过程。超晶格的调谐允许控制快速一阶过程相对于较慢的二阶过程的效果。使用密度矩阵重整化群方法，我们提供了典型的实验可用的观测量的演变。通过海森堡模型的描述的有效性，取决于哈伯德模型的参数，数值和分析研究。分析也是由最近的实验[S. Foelling等人，Nature 448，1029（2007）; S. Trotzky等人，Sience 319，295（2008）]，其中实现了在隔离双阱中具有超冷玻色子原子的相干双粒子动力学。我们为下一步的研究工作提供了理论基础，即双阱耦合后相干多粒子动力学的观测。与孤立双阱的情况相反，可以观察到局部可观测量的弛豫。在此装置中，玻色-哈伯德模型和海森堡模型之间的可调性可以用来实验研究不可积和Bethe不可积模型平衡过程的差异。我们表明，海森堡模型中的弛豫连接到一个相位平均效应，这是在典型的散射驱动的热化在不可积模型相反。我们讨论了通过绝热调节超晶格参数来制备磁性基态。
英文摘要：
We study how well magnetic models can be implemented with ultracold bosonic atoms of two different hyperfine states in an optical superlattice. The system is captured by a two-species Bose-Hubbard model, but realizes in a certain parameter regime actually the physics of a spin-1/2 Heisenberg magnet, describing the second order hopping processes. Tuning of the superlattice allows for controlling the effect of fast first order processes versus the slower second order ones. Using the density-matrix renormalization-group method, we provide the evolution of typical experimentally available observables. The validity of the description via the Heisenberg model, depending on the parameters of the Hubbard model, is studied numerically and analytically. The analysis is also motivated by recent experiments [S. Foelling et al., Nature 448, 1029 (2007); S. Trotzky et al., Sience 319, 295 (2008)] where coherent two-particle dynamics with ultracold bosonic atoms in isolated double wells were realized. We provide theoretical background for the next step, the observation of coherent many-particle dynamics after coupling the double wells. Contrary to the case of isolated double wells, relaxation of local observables can be observed. The tunability between the Bose-Hubbard model and the Heisenberg model in this setup could be used to study experimentally the differences in equilibration processes for nonintegrable and Bethe ansatz integrable models. We show that the relaxation in the Heisenberg model is connected to a phase averaging effect, which is in contrast to the typical scattering driven thermalization in nonintegrable models. We discuss the preparation of magnetic groundstates by adiabatic tuning of the superlattice parameters.
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