Theoretical Analysis of Photonic Resonances in Spectroscopic Measurements of a Kerr Nonlinear Resonator

The Kerr parametric oscillator (KPO) has recently attracted considerable attention from the perspective of its applications to quantum information processing, and understanding its properties is an important challenge. Spectroscopic measurements serve as an effective means of elucidating detailed information about the system, such as the energy-level structure and the transition matrix elements of the KPO. Conventional spectroscopy requires the drive frequency to match an energy spacing with a nonzero transition matrix element. In recent years, a phenomenon called photonic resonance (PR) has been theoretically predicted in KPO spectroscopy. Specifically, resonance occurs under the condition that the detuning is set to n/2 times the Kerr nonlinearity, where n is a natural number. However, under this condition the transition matrix element vanishes, and thus the mechanism by which photonic resonance (PR) arises has remained unclear. In this work, we aim to elucidate the physical origin of PR observed in KPO spectroscopy. We first performed theoretical calculations and experiments of spectroscopic measurements, confirming that PR can indeed be observed and that the theoretical and experimental results are in qualitative agreement. We then carried out an analytical study under the assumption of an ideal noiseless environment. Our analysis revealed that, although the transition matrix element of the external field expressed in the system's energy eigenbasis is zero, higher-order perturbative effects induce Rabi oscillations between the ground and excited states. Furthermore, numerical simulations in a time domain including the effect of decoherence demonstrated that coherent oscillations decay, leading to the appearance of PR.