Bose-Hubbard hopping due to resonant Rayleigh scattering.

We show theoretically that dynamic behavior of light confined in the modes of a nonlinear optical ring cavity characterized by resonant Rayleigh scattering can be described using the Bose-Hubbard model. Nonlinear interaction between clockwise and counterclockwise optical modes results in instability and intermode hopping occurring at a rate defined by the frequency separation of the Rayleigh doublet harmonics. Hopping may lead to an instability and breathing behavior of a Kerr frequency comb observed in the cavity.