We study the nonlinear phase response of a microring resonator coupled to a bus waveguide and the use of this nonlinear phase shift to store information in the microring resonator and enhance the switching characteristics of a Mach–Zehnder interferometer (MZI). By introducing coupling between adjacent microring resonators, the switching characteristics of the MZI can be exponentially enhanced as a function of the number of microring resonators, when compared to the linear enhancement for uncoupled resonators. With only a few moderate-finesse microring resonators, the switching power can be reduced to attowatt level, allowing for photonic switching devices that operate at single-photon level in ordinary optical waveguides.