Supersolids are characterized by the counterintuitive coexistence of superfluid and crystalline order. Here we study a supersolid phase emerging in the steady state of a driven-dissipative system. We consider a transversely pumped Bose-Einstein condensate trapped along the axis of a ring cavity and coherently coupled to a pair of degenerate counterpropagating cavity modes. Above a threshold pump strength the interference of photons scattered into the two cavity modes results in an emergent superradiant lattice, which spontaneously breaks the continuous translational symmetry towards a periodic atomic pattern. The crystalline steady state inherits the superfluidity of the Bose-Einstein condensate, thus exhibiting genuine properties of a supersolid. A gapless collective Goldstone mode correspondingly appears in the superradiant phase, which can be nondestructively monitored via the relative phase of the two cavity modes on the cavity output. Despite cavity-photon losses the Goldstone mode remains undamped, indicating the robustness of the supersolid phase.

中文翻译：

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环形腔中的驱动耗散超固体

超固体的特征在于超流体和结晶顺序的反直觉共存。在这里，我们研究在驱动耗散系统的稳态下出现的超固相。我们考虑了沿环形腔轴捕获的横向泵送的玻色-爱因斯坦冷凝物，并与一对简并的反向传播腔模相干耦合。高于阈值泵浦强度时，散射到两个腔模中的光子的干扰会导致出现超辐射晶格，该晶格自发地将连续的平移对称性破坏为周期性原子模式。晶体稳态继承了玻色-爱因斯坦冷凝物的超流动性，因此表现出超固体的真正性质。无间隙的集体戈德斯通模式相应地出现在超辐射阶段，可以通过腔体输出上的两个腔体模式的相对相位进行无损监控。尽管有腔光子损失，但戈德斯通模态仍未衰减，表明超固相的稳健性。