Bistability of Exciton-Photon Microcavities in the Ultrastrong-Coupling Regime

We investigate a coherently driven exciton--photon microcavity with Kerr nonlinearity in the ultrastrong-coupling regime.

When the lower and upper polariton branches are well separated in energy, the full Hopfield--Rabi--Kerr model reduces to an effective single-mode description of the lower polariton.

We analyze the stability of the lower-polariton steady states.

We show that the resulting bistability is qualitatively similar to that in the strong-coupling regime.

However, in the ultrastrong-coupling regime counter-rotating processes and the diamagnetic $A^{2}$ term renormalize the polariton spectrum and composition, changing the effective detuning $\tilde{\Delta}_{1}$ and nonlinearity $U_{\mathrm{LP}}$ $g$-dependency beyond the strong-coupling (RWA) picture.

As a result, although the semiclassical bistability criterion keeps its standard Kerr--oscillator form, the turning points and hysteresis window are shifted relative to the strong-coupling prediction.