We report experimental evidence of the interaction between intersubband polaritons and longitudinal optical phonons in non-dispersive mid-infrared cavities, under resonant optical injection. The light emission originating from spontaneous polariton-phonon scattering is observed at a frequency corresponding to an energy shift of one phonon below the pump frequency. Given the extremely low spontaneous scattering rate, we employ a custom-developed quantum mechanical model to numerically demonstrate the feasibility to stimulate such process using a pump-probe scheme. Based on this analysis, we identify a set of experimental conditions under which optical gain may be realized in a mid-infrared intersubband polaritonic system.

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