We explore the consequences of disorder on phase coherence in the Mott insulator phases in an optical lattice. Few bosons with contact interaction in small optical lattice can feature varieties of insulating phases—weakly interacting Mott in deep lattice, maximally fragmented and strongly interacting Mott in intermediate lattice, weak Mott with double filling and intrawell coherence, fermionized Mott with strong intrawell coherence. Utilization of the multiconfigurational time-dependent Hartree method for bosons to solve the many-boson Schrödinger equation, facilitates to understand the microscopic effect of disorder on the different kinds of Mott phases in the primary lattice. The many-body properties are analyzed by distinct measures of the reduced one-body density in real and momentum space, fragmentation, order parameter, variance of spatial single-shot measurements, compressibility, and the Glauber normalized correlation functions. We find very complex competition of localization due to disorder and Mott correlation. We observe distinct response of four different Mott phases in the disordered lattice. When the weakly interacting Mott exhibits the Bose glass phase, the strongly correlated and fully fragmented Mott exhibits leakage, melting and central localization. In contrast, weak Mott with double filling which is a spatially separated dimer in each site, exhibits only some dissociation of intrawell coherence and assist in the development of interwell coherence in the presence of strong disorder. For the fermionized Mott, when the density in each well is fragmented, strong disorder interferes with the intrawell correlation and the characteristic dip in each site starts to disappear leading to simple Mott localization with a pair of bosons.

中文翻译：

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一维无序晶格中的强相互作用玻色子：扭曲 Mott 相的相位相干性


我们探讨了无序对光晶格中 Mott 绝缘体相相干性的影响。在小光晶格中具有接触相互作用的少数玻色子可以具有多种绝缘相——深晶格中的弱相互作用 Mott，中间晶格中最大碎裂和强相互作用的 Mott，具有双重填充和阱内相干性的弱 Mott，具有强阱内相干性的费米离子化 Mott。利用玻色子的多构型瞬态 Hartree 方法求解多玻色子薛定谔方程，有助于理解无序对初级晶格中不同种类的 Mott 相的微观影响。通过对实空间和动量空间中降低的单体密度、碎裂、阶参数、空间单脉冲测量的方差、可压缩性和 Glauber 归一化相关函数的不同测量来分析多体特性。我们发现由于无序和 Mott 相关性，定位竞争非常复杂。我们在无序晶格中观察到四种不同 Mott 相的不同响应。当弱相互作用的 Mott 表现出 Bose 玻璃相时，强相关和完全碎裂的 Mott 表现出泄漏、熔化和中心定位。相比之下，具有双重填充的弱 Mott 在每个位点都是空间分离的二聚体，仅表现出井内相干性的一些解离，并有助于在强无序存在下井间相干性的发展。对于费米离子化的 Mott，当每个孔中的密度碎裂时，强烈的无序会干扰孔内相关性，并且每个位点的特征性下降开始消失，从而导致带有一对玻色子的简单 Mott 定位。