Stationary inversion of a two level system coupled to an off-resonant cavity with strong dissipation.

We present an off-resonant excitation scheme that realizes pronounced stationary inversion in a two level system. The created inversion exploits a cavity-assisted two-photon resonance to enhance the multiphoton regime of nonlinear cavity QED and survives even in a semiconductor environment, where the cavity decay rate is comparable to the cavity-dot coupling rate. Exciton populations of greater than 0.75 are obtained in the presence of realistic decays and pure dephasing. Quantum trajectory simulations and master equation calculations help elucidate the underlying physics and delineate the limitations of a simplified rate equation model. Experimental signatures of inversion and multiphoton cavity QED are predicted in the fluorescence intensity and second-order correlation function measured as a function of drive power.