Fig. 3
From: Coherent microwave-photon-mediated coupling between a semiconductor and a superconducting qubit
DQD-transmon interaction mediated by virtual photon exchange in the SQUID array resonator. a Energy level diagram of the DQD-transmon qubit coupling mediated via dispersive interaction with the SQUID array resonator (red line). The DQD excitation \((\sigma _{{\mathrm{DQD}}}^\dagger |0\rangle )\), the transmon excitation \((a_{{\mathrm{tr}}}^\dagger |0\rangle )\) and the SQUID array resonator excitation \((a_{{\mathrm{Sq}}}^\dagger |0\rangle )\) are shown, together with their hybridized states |Ψs,a〉 and the system vacuum state |0〉 = |0〉Sq ⊗ |g〉tr ⊗ |g〉DQD. b Left: spectroscopy of the DQD qubit interacting with the transmon. Phase Δϕ = Arg[S11] of a fixed frequency measurement tone ωp/2π = 6.5064 GHz = ωr,50Ω/2π reflected off the 50 Ω CPW read-out resonator vs. transmon qubit spectroscopy frequency ωs and DQD qubit detuning δ [(c) the flux through the SQUID loop of the transmon Φtr]. Right: phase Δϕ = Arg[S11] response at the DQD detuning δ [(c) at the flux Φtr] indicated by the black arrows in left panel showing a coupling splitting of 2J ~20.8 ± 0.3 MHz [2J ~21.1 ± 0.2 MHz]. d Pulse protocol for the population transfer between the transmon and the DQD charge qubit. ρ(t) indicates the density matrix of the coupled transmon-DQD system during the interaction time Δτ and \(\tilde \omega _{{\mathrm{r,50\Omega }}} = \omega _{{\mathrm{r,50\Omega }}} + g_{{\mathrm{tr,50\Omega }}}^2/{\mathrm{\Delta }}_{{\mathrm{tr,50\Omega }}}\). τ0 is a finite time difference between the preparation pulse and the flux pulse. e Average transmon excited state population Pe,tr (each data point is the intergrated average over 50,000 repetitions of the experiment), as a function of the flux pulse length Δτ and normalized flux pulse amplitude A/A0. f Transmon excited state population Pe,tr vs. Δτ for a flux pulse amplitude of A/A0 = 0.55, for which the transmon is approximately in resonance with the DQD (ωtr/2π ~ωDQD/2π=3.660 GHz). ωr,Sq/2π = 4.060GHz and ωr,50Ω/2π = 6.5048 GHz. The red line is a fit to a Markovian master equation model (see Supplementary Note 6 for more details)
