  We study optical bistable behavior of a Rydberg electromagnetically-induced
transparency (EIT) atomic medium in a unidirectional optical ring-cavity. Due
to strong van del Waal (vdW) interactions between the atoms, both optical
nonlinear dispersion and nonlinear absorption coefficients are enhanced
substantially. Under the condition of two-photon on resonance, we show that
probe one-photon detuning can change the phase of the third order nonlinearity
coefficient, which tunes the character of the optical bistability within
different ratios of dispersive and absorptive types. This enables the
single-photon control over photonic devices for further manipulation of light
other than switches and transistors. More interestingly, we predict appearance
of a scaling phenomena for optical bistabilities with the factors of coupling
Rabi frequency and atomic density. Additionally, we also discuss the influence
of the cavity detuning and the mirror transmission coefficient on the optical
bistable behavior. The strong bistable feature provides a good ingredient for
realizing all-optical logic gate devices in optical computing.
