Restoring Bloch's Theorem for Cavity Exciton Polaron-Polaritons

In recent years, cavity and polariton physics have advanced dramatically, both experimentally and theoretically. However, as theoretical studies seek to explain increasingly more complicated physical systems, the computational cost grows exponentially. In condensed matter physics, Bloch's theorem drastically simplifies the complexity of calculating periodic systems by allowing each wavevector of the total Hamiltonian to be treated independently, yet this structure breaks down upon interactions with photonic and phononic fields.

We introduce a symmetry-informed representation for hybrid photon-exciton-phonon quantum electrodynamics Hamiltonians that restores Bloch's theorem. By taking advantage of the symmetries of the interactions between these degrees of freedom, we can create a new quantum number, which turns our Hamiltonian block-diagonal. We leverage this to calculate band structures and dielectric functions, where we discover that the exchange of momentum between these degrees of freedom can break the inversion symmetry of the exciton, unlocking previously forbidden optical transitions. We expect this representation has far-reaching implications for strongly coupled fermion-boson systems, enabling investigations that elucidate materials properties in strong coupling with applications in tuning electronic/optical properties, enhancing coherent transport, and unlocking symmetry-forbidden transitions.