The classical and quantum performance of cavity-parametric amplifiers employing Kerr nonlinearites with two-photon loss

Two photon loss mechanisms often accompany a Kerr nonlinearity. The kinetic inductance exhibited by superconducting transmission lines provides an example of a Kerr-like nonlinearity that is accompanied by a nonlinear resistance of the two-photo absorptive type. Such nonlinear dissipation can degrade the performance of amplifiers and mixers employing a Kerr-like nonlinearity as the gain or mixing medium. As an aid for parametric amplifier design, we provide a quantum analysis of a cavity parametric amplifier employing a Kerr nonlinearity that is accompanied by a two-photon absorptive loss. Because of their use for diagnostic purposes, we obtain expressions for the pump amplitude within the cavity, the reflection coefficient for the pump amplitude reflected off of the cavity, the parametric gain, and the intermodulation gain. Expressions that show the computation of the degree of squeezing are also presented.