Generalized Bloch's Theorem for Cavity Exciton Polaron-Polaritons

TL;DR

This paper extends Bloch's theorem to cavity exciton polaron-polaritons, allowing for symmetry-preserving analysis of their dispersions and optical responses in strong coupling regimes.

Contribution

It introduces a generalized Bloch theorem applicable to excitons coupled with cavity photons and phonons, preserving translational symmetry without approximations.

Findings

Hamiltonian becomes block diagonal in the symmetry-adapted frame.

Dispersions and optical responses of cavity exciton polaron-polaritons are derived.

Framework enables investigation of material properties in strong coupling.

Abstract

We show that excitons coupled to cavity photons and phonons admit a generalized Bloch theorem when formulated for the conserved total crystal momentum. In minimal-coupling and Fr\"ohlich representations, the interchange of momenta between fermions and bosons breaks crystalline excitons' translational symmetry. In our symmetry-adapted frame, the Hamiltonian becomes block diagonal, without invoking approximations. The resulting formulation yields dispersions and optical responses of cavity exciton polaron-polaritons, enabling investigations that elucidate material properties in strong coupling.