Dephasing due to intermode coupling in superconducting stripline resonators

The nonlinearity exhibited by the kinetic inductance of a superconducting stripline couples stripline resonator modes together in a manner suitable for quantum nondemolition measurement of the number of photons in a given resonator mode. Quantum nondemolition measurement is accomplished by coherently driving another resonator mode, referred to as the detector mode, and measuring its response. We show that the sensitivity of such a detection scheme is directly related to the dephasing rate induced by such an intermode coupling. We show that high sensitivity is expected when the detector mode is driven into the nonlinear regime and operated close to a point where critical slowing down occurs.