Recent experimental advances to create tunable synthetic spin-orbit coupling (SOC) in ultracold gases provide new possibilities to access fruitful spin-orbit coupled quantum many-body physics. In this paper, we demonstrate that the combined effect of two-dimensional (2D) SOC and one-dimensional (1D) optical lattice in interacting bosons can provide an alternative scheme in ultracold gases to achieve the crossover of the commensurate-incommensurate supersolid ground state “with respect to the background optical lattice.” Interestingly, it is shown that the anharmonicity arising from the lattice potential leads to the “pin” effect and make the ground-state break the continuous translational symmetry along the direction perpendicular to the 1D lattice, whereas the competition between the lattice period and the SOC length results in the crossover of commensurate-incommensurate ground state along the direction of 1D lattice with discrete translational symmetry breaking. Such a combined effect of SOC and optical lattice, thus, induces a new 2D periodic pattern in the ground state, accompanying with nonzero 2D superfluid density characterizing the supersolid nature in 2D of the ground state. Furthermore, a skyrmion-anti-skyrmion lattice is found associated with the appearance of such supersolid ground state, indicating its topological nontrivial properties. Experimental signature of our proposed supersolid ground state is also predicted by means of the time-of-flight measurement.

中文翻译：

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一维光学晶格中自旋轨道耦合的玻色-爱因斯坦凝聚物的等量-不等量超固态基态

在超冷气体中创建可调谐的合成自旋轨道耦合（SOC）的最新实验进展为访问硕果累累的自旋轨道耦合量子多体物理学提供了新的可能性。在本文中，我们证明了二维（2D）SOC和一维（1D）光学晶格在相互作用的玻色子中的组合效应可为超冷气体提供一种替代方案，以实现相称相称的超固态基态的交换“关于背景光学晶格。” 有趣的是，表明晶格电势引起的非谐性导致“ pin”效应并使基态沿垂直于一维晶格的方向破坏连续的平移对称性，而晶格周期与SOC长度之间的竞争导致了沿一维晶格方向的相称不相称基态的交叉，具有离散的平移对称性破裂。因此，SOC和光学晶格的这种组合效应会在基态下诱导出新的2D周期性模式，并伴随着非零的2D超流体密度，该密度表征了基态2D的超固体质。此外，发现了与这种超固态基态的外观相关联的天敌离子-反天敌离子晶格，表明其拓扑非平凡性质。我们建议的超固态基态的实验特征还可以通过飞行时间测量来预测。因此，SOC和光学晶格的这种组合效应会在基态下诱导出新的2D周期性模式，并伴随着非零的2D超流体密度，该密度表征了基态2D的超固体性质。此外，发现与这种超固态基态的外观相关联的天敌离子-抗天敌离子的晶格，表明其拓扑非平凡的性质。我们建议的超固态基态的实验特征还可以通过飞行时间测量来预测。因此，SOC和光学晶格的这种组合效应会在基态下诱导出新的2D周期性模式，并伴随着非零的2D超流体密度，该密度表征了基态2D的超固体性质。此外，发现与这种超固态基态的外观相关联的天敌离子-抗天敌离子的晶格，表明其拓扑非平凡的性质。我们建议的超固态基态的实验特征还可以通过飞行时间测量来预测。表明其拓扑非平凡特性。我们建议的超固态基态的实验特征还可以通过飞行时间测量来预测。表明其拓扑非平凡特性。我们建议的超固态基态的实验特征还可以通过飞行时间测量来预测。