Mott polaritons in cavity-coupled quantum materials

We show that strong electron-electron interactions in quantum materials can give rise to electronic transitions that couple strongly to cavity fields, and collective enhancement of these interactions can result in ultrastrong effective coupling strengths. As a paradigmatic example we consider a Fermi-Hubbard model coupled to a single-mode cavity and find that resonant electron-cavity interactions result in the formation of a quasi-continuum of polariton branches. The vacuum Rabi splitting of the two outermost branches is collectively enhanced and scales with USD g_{\text{eff}}\propto\sqrt{2L} USD, where USD L USD is the number of electronic sites, and the maximal achievable value for USD g_{\text{eff}} USD is determined by the volume of the unit cell of the crystal. We find that USD g_{\text{eff}} USD for existing quantum materials can by far exceed the width of the first excited Hubbard band. This effect can be experimentally observed via measurements of the optical conductivity and does not require ultrastrong coupling on the single-electron level. Quantum correlations in the electronic ground state as well as the microscopic nature of the light-matter interaction enhance the collective light-matter interaction compared to an ensemble of independent two-level atoms interacting with a cavity mode