Quantum linewidth limitation of a laser stabilized with a nonlinear microcavity

We show that the linewidth of a laser locked to an optical cavity characterized with nonzero optical cubic nonlinearity is restricted by the value of the nonlinear frequency shift of the cavity mode per single photon localized in the mode. This effect is masked by the fundamental thermodynamic noise in monolithic microcavities. The quantum limit of the linewidth can be measured using two independent lasers separately locked to spatially overlapping modes of the nonlinear resonator.