Formation of Cavity-Polaritons via High-Order Van Hove Singularities

Abstract

We consider polaritons formed by hybridizing a continuum of interband particle-hole excitations of an insulating phase with a cavity photon at subgap frequencies, where absorption is suppressed. The strength of the hybridization is driven by the Van Hove singularity in the joint density of states (JDOS) at the band gap: the stronger the singularity, the more a photon is hybridized with the interband transitions. In order to increase the singularity and thus the polariton hybridization without absorption, we propose to engineer a nonparabolic momentum dispersion of the bands around the gap in order to implement a high-order Van Hove singularity (HOVHS) in the JDOS. Ultracold atoms in tunable optical lattices are an ideal platform to engineer two-dimensional gapped phases with nontrivial band dispersions at the gap. Moreover, the intrinsic noninteracting nature of polarized fermionic atoms prevents the emergence of subgap excitations, which are common in solid-state systems and could otherwise spoil the absence of absorption below the gap. Our findings identify band-engineering at the gap edge as a promising route for polariton control with applications in quantum nonlinear optics.

21 pages, 12 figures