Raman-phonon-polariton condensation in a transversely pumped cavity

Phonon polaritons are hybrid states of light and matter that are typically realised when optically active phonons couple strongly to photons. We suggest a new approach to realising phonon polaritons, by employing a transverse-pumping Raman scheme, as used in experiments on cold atoms in optical cavities. This approach allows hybridisation between an optical cavity mode and any Raman-active phonon mode. Moreover, this approach enables one to tune the effective phonon-photon coupling by changing the strength of the transverse pumping light. We show that such a system may realise a phonon-polariton condensate. To do this, we find the stationary states and use Floquet theory to determine their stability. We thus identify distinct superradiant and lasing states in which the polariton modes are macroscopically populated. We map out the phase diagram of these states as a function of pump frequencies and strengths. Using parameters for transition metal dichalcogenides, we show that realisation of these phases may be practicably obtainable. The ability to manipulate phonon mode frequencies and attain steady-state populations of selected phonon modes provides a new tool for engineering correlated states of electrons.