A transmon of transition frequency is coupled to a resonator of frequency with coupling

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Quantum Information and Technology, Ch Superconducting qubits and circuit QED

Problem

A transmon of transition frequency ωq\omega_q is coupled to a resonator of frequency ωr\omega_r with coupling g/2π=8.0 MHzg/2\pi = 8.0\,\mathrm{MHz}, in the Jaynes-Cummings model with the rotating-wave approximation. The detuning is Δ/2π=(ωq−ωr)/2π=24.0 MHz\Delta/2\pi = (\omega_q-\omega_r)/2\pi = 24.0\,\mathrm{MHz}. ((a)) Diagonalise the one-excitation block {∣1,0⟩,∣0,1⟩}\{|1,0\rangle,|0,1\rangle\} and give the frequency splitting between the two dressed states. ((b)) State whether this system is in the strong-coupling regime, given that its resonator and qubit loss rates are both below 1 MHz1\,\mathrm{MHz}.

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