Photon-Mediated Peierls Transition of a 1D Gas in a Multimode Optical Cavity

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.

Figure 1

Schematic of our system. A gas of interacting atoms is placed in a confocal optical cavity that supports many degenerate spatial modes. A transverse pump (blue) along $\widehat{y}$ scatters photons off the atoms (red) into the multimode cavity field (blue). The gas is confined by a 2D optical lattice (purple) and offset from $y=0$ to avoid mirror-image interactions [12]. The amplitude and phase of the light is imaged via holographic reconstruction of a spatial heterodyne signal formed by interfering part of the pump with the emission.

Figure 2

Left: simulated intracavity field amplitude at the atoms (a) below and (c) far above the transition, with a density wave of wave vector $k=\pi /(0.6w_0)$ in the TG limit. Right: cavity emission (b) below and (d) above the transition. Emission from a confocal cavity contains both an image of the atomic density (horizontal blue pattern) and its Fourier transform (vertical blue and orange patterns). These can be measured by holographic reconstruction of a spatial heterodyne image [7, 14]. The scale bar in (a) shows the Gaussian waist $w_0$ of the cavity.