Fig. 2: Quantum Rabi-like splitting.

Quantum Rabi-like splitting between a single-photon and a two-photon Fock state. a Measured and calculated transmission spectra of the one-photon line of the n = 1 mode of the resonator as a function of the flux offset. b Measured and calculated transmission spectra showing the excitation of both the two-photon state of the n = 1 mode and the one-photon state of the n = 2 mode of the resonator. An avoided-level crossing between these two lines is clearly visible. From the fitting, we obtain the Rabi frequency for the one–two-photon coupling g_eff/2π = 59 MHz, the loss rate due to the input–output ports (κ_in + κ_out)/2π = 2.6 MHz, the internal loss rate κ_int/2π = 10.4 MHz [total loss rate of the resonator κ_tot/2π = (κ_in + κ_out + κ_int)/2π = 13 MHz], the intrinsic loss rate of the qubit κ_q/2π = 200 MHz, and the pure dephasing rate of the qubit κ_q,dep/2π = 200 MHz (the last two have a very weak influence on the calculated spectra).