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We report the spectroscopic characterization of a Kerr parametric oscillator(KPO) based on the measurement of its reflection coefficient under a two-photondrive induced by flux modulation. The measured reflection spectra show goodagreement with numerical simulations in term of their dependence on thetwo-photon drive amplitude. The spectra can be interpreted as changes insystem's eigenenergies, transition matrix elements, and the population of theeigenstates, although the linewidth of the resonance structure is not fullyexplained. We also show that the drive-amplitude dependence of the spectra canbe explained analytically by using the concepts of Rabi splitting and the Starkshift. By comparing the experimentally obtained spectra with theory, we showthat the two-photon drive amplitude at the device can be precisely determined,which is important for the application of KPOs in quantum informationprocessing.

Spectroscopy of flux-driven Kerr parametric oscillators by reflection coefficient measurement