The Peierls instability toward a charge density wave is a canonical example of phonon-driven strongly correlated physics and is intimately related to topological quantum matter and exotic superconductivity. We propose a method for realizing an analogous photon-mediated Peierls transition, using a system of one-dimensional tubes of interacting Bose or Fermi atoms trapped inside a multimode confocal cavity. Pumping the cavity transversely engineers a cavity-mediated metal-to-insulator transition in the atomic system. For strongly interacting bosons in the Tonks-Girardeau limit, this transition can be understood (through fermionization) as being the Peierls instability. We extend the calculation to finite values of the interaction strength and derive analytic expressions for both the cavity field and mass gap. They display nontrivial power law dependence on the dimensionless matter-light coupling.

中文翻译：

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一维气体在多模光学腔中的光子介导的Peierls跃迁。

Peierls对电荷密度波的不稳定性是声子驱动的强相关物理学的典型示例，并且与拓扑量子物质和奇特的超导性密切相关。我们提出了一种方法，该方法使用一个被困在多模共焦腔内的相互作用的Bose或Fermi原子的一维管系统来实现类似的光子介导的Peierls跃迁。横向泵送空腔可在原子系统中设计出空腔介导的金属到绝缘体的过渡。对于在Tonks-Girardeau极限中强烈相互作用的玻色子，可以将这种转变（通过费米化作用）理解为Peierls不稳定性。我们将计算扩展到相互作用强度的有限值，并导出腔场和质量间隙的解析表达式。