  Superconducting parametrons in the single-photon Kerr regime, also called
KPOs, have been attracting increasing attention in terms of their applications
to quantum annealing and universal quantum computation. It is of practical
importance to obtain information of superconducting parametrons operating under
an oscillating pump field. Spectroscopy can provide information of a
superconducting parametron under examination, such as energy level structure,
and also useful information for calibration of the pump field. We theoretically
study the reflection spectroscopy of superconducting parametrons, and develop a
method to obtain the reflection coefficient. We present formulae of the
reflection coefficient, the nominal external and the internal decay rates, and
examine the obtained spectra. It is shown 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.
