Xing Yan, Zhao Xuedong, Lü Zhe, Liu Shutian, Zhang Shou, Wang Hong-Fu
Opt Express. 2021 Nov 22;29(24):40428-40446. doi: 10.1364/OE.446007.
We theoretically and systematically investigate Anderson localization of two bosons with nearest-neighbor interaction in one dimension under short- and long-time scales, two types of disorders, and three types of initial states, which can be directly observed in linear disordered photonic lattices via two experimentally measurable physical quantities, participation ratio and spatial correlation. We find that the behavior of localization characterized by the participation ratio depends on the strength of interaction and the type of disorder and initial condition. Two-boson spatial correlation reveals more novel and unique features. In the ordered case, two types of two-boson bindings and bosonic "fermionization" are shown, which are intimately attributed to the band structure of the system. In the disordered case, the impact of interaction on the two-boson Anderson localization is reexamined and the joint effect of disorder and interaction is addressed. We further demonstrate that the independence of the participation ratio or spatial correlation on the sign of interaction can be eliminated by employing an initial state that breaks one of two specific symmetries. Finally, we elucidate the relevant details of the experimental implementation in a two-dimensional linear photonic lattice.
我们从理论上系统地研究了一维空间中具有最近邻相互作用的两个玻色子在短时间和长时间尺度、两种无序类型以及三种初始状态下的安德森局域化，这可以通过线性无序光子晶格中的两个可实验测量的物理量——参与率和空间相关性直接观察到。我们发现，以参与率表征的局域化行为取决于相互作用强度、无序类型和初始条件。双玻色子空间相关性展现出更多新颖独特的特征。在有序情况下，展示了两种双玻色子束缚态和玻色子“费米化”，这与系统的能带结构密切相关。在无序情况下，重新审视了相互作用对双玻色子安德森局域化的影响，并探讨了无序和相互作用的联合效应。我们进一步证明，通过采用打破两种特定对称性之一的初始状态，可以消除参与率或空间相关性对相互作用符号的独立性。最后，我们阐明了二维线性光子晶格中实验实现的相关细节。
