Coherent microwave-photon-mediated coupling between a semiconductor and a superconducting qubit

Abstract

Semiconductor qubits rely on the control of charge and spin degrees of freedom of electrons or holes confined in quantum dots. They constitute a promising approach to quantum information processing, complementary to superconducting qubits. Here, we demonstrate coherent coupling between a superconducting transmon qubit and a semiconductor double quantum dot (DQD) charge qubit mediated by virtual microwave photon excitations in a tunable high-impedance SQUID array resonator acting as a quantum bus. The transmon-charge qubit coherent coupling rate (~21 MHz) exceeds the linewidth of both the transmon (~0.8 MHz) and the DQD charge qubit (~2.7 MHz). By tuning the qubits into resonance for a controlled amount of time, we observe coherent oscillations between the constituents of this hybrid quantum system. These results enable a new class of experiments exploring the use of two-qubit interactions mediated by microwave photons to create entangled states between semiconductor and superconducting qubits.

Fig. 1

Sample and simplified circuit diagram. a False color optical micrograph of the device showing the substrate (dark gray), the Al superconducting structures forming the groud plane (light gray), the DQD Au gate leads (yellow), the SQUID array resonator (red), its microwave feedline (green), the single island transmon (orange), its readout 50 Ω coplanar waveguide resonator (blue), and the flux line (purple). b Enlarged view of the sample area enclosed by the blue dashed line in panel (a). c Enlarged view of the coupling side of the SQUID array. d Electron micrograph of the DQD showing its electrostatic top gates (Al-light gray) and the plunger gate coupled to the SQUID array (red). e Electron micrograph of the transmon SQUID. f Circuit diagram schematically displaying the DQD [with its source (S) and drain (D) contact], capacitively coupled to the SQUID array resonator, which in turn is coupled to the transmon. The transmon and the SQUID array are respectively capacitively coupled to a 50 Ω CPW resonator and microwave feedline. Their resonance frequencies can be tuned by using a flux line and a coil schematically shown in the circuit diagram. The color code is consistent with the optical micrographs

Fig. 2

Resonant interaction between the DQD charge qubit, the SQUID array resonator and the transmon. a Energy level diagram of the DQD-SQUID array-transmon system for the bias point considered in panel (b). The energy levels are colored in accordance with the code used in Fig. 1. b Reflectance $\mid S_{11}^{\mathrm{Sq}}\mid$ of the SQUID array resonator hybridized with the transmon and DQD as a function of the DQD detuning δ at the bias point discussed in the main text. Red dots are obtained by numerical diagonalization of the system Hamiltonian [see Eq. (1) in Supplementary Note 2], using parameters extracted from independent spectroscopy measurements

Fig. 3

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 $\left({\sigma }_{\mathrm{DQD}}^{†}\mid 0⟩\right)$, the transmon excitation $\left(a_{\mathrm{tr}}^{†}\mid 0⟩\right)$ and the SQUID array resonator excitation $\left(a_{\mathrm{Sq}}^{†}\mid 0⟩\right)$ are shown, together with their hybridized states |Ψ_s,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 ω_p/2π = 6.5064 GHz = ω_r,50Ω/2π reflected off the 50 Ω CPW read-out resonator vs. transmon qubit spectroscopy frequency ω_s and DQD qubit detuning δ [(c) the flux through the SQUID loop of the transmon Φ_tr]. Right: phase Δϕ = Arg[S₁₁] response at the DQD detuning δ [(c) at the flux Φ_tr] 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 P_e,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 P_e,tr vs. Δτ for a flux pulse amplitude of A/A₀ = 0.55, for which the transmon is approximately in resonance with the DQD (ω_tr/2π ~ω_DQD/2π=3.660 GHz). ω_r,Sq/2π = 4.060GHz and ω_r,50Ω/2π = 6.5048 GHz. The red line is a fit to a Markovian master equation model (see Supplementary Note 6 for more details)