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

We consider polaritons formed by hybridizing particle-hole excitations of an insulating phase with a cavity photon at sub-gap 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 non-parabolic 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 non-trivial band dispersions at the gap.

Moreover, the intrinsic non-interacting nature of polarized fermionic atoms prevents the emergence of sub-gap 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.