Single photon optical bistability

We investigate the bistability in a small Fabry-Perot interferometer (FPI) with the optical wavelength size cavity, the nonlinear Kerr medium and only a few photons, on average, excited by the external quantum field. Analytical expressions for the stationary mean photon number, the bistability domain, the field and the photon number fluctuation spectra are obtained. Multiple stationary states of the FPI cavity field with different spectra are possible at realistic conditions, for example, in the FPI with the photonic crystal cavity and the semiconductor-doped glass nonlinear medium.