Theory of reflection spectroscopy for superconducting quantum parametrons

Superconducting parametrons in the single-photon Kerr regime, also called KPOs, have been attracting increasing attention in terms of their applications to quantum computations. Theory of spectroscopy of prametrons is needed for obtaining information such as energy level structure and coupling strength between the energy levels from experiments. In this talk, we report the results of our theoretical study on the reflection spectroscopy of superconducting parametrons. We show formulae of the reflection coefficient, the nominal external and internal decay rates. We present that the difference of the populations of energy levels manifests itself as a dip or peak in the amplitude of the reflection coefficient, and one can directly extract the coupling strength between the energy levels by measuring the nominal decay rates when the pump field is sufficiently large.