Inter-transition interference in spectrum of Kerr parametric oscillators

Abstract A Kerr parametric oscillator (KPO) is a Kerr-nonlinear resonator driven parametrically, which can serve as a qubit in quantum information processing. Spectroscopy using a weak probe field provides a practical method for extracting system parameters. In this work, we theoretically investigate reflection and transmission measurements of two-photon and four-photon KPOs, introducing interference effects between inter-level transitions. Because KPOs typically exhibit energy-level degeneracy, a probe field can simultaneously resonate with multiple inter-level transitions. We extend the previous theory of reflection measurements by incorporating the interaction between inter-level transitions and off-diagonal elements of the density matrix which had previously been neglected. We demonstrate that interference among these transitions substantially modifies the spectrum. We identify the conditions for the interference, as well as those under which the off-diagonal elements of the density matrix affect the spectrum. The theory is also generalized to transmission measurements, and is applicable to a broad class of systems beyond KPOs.