Vacuum Rabi Splitting in a Semiconductor Circuit QED System

Vacuum Rabi splitting is demonstrated in a GaAs double quantum dot system coupled with a coplanar waveguide resonator. The coupling strength $g$, the decoherence rate of the quantum dot $\gamma$, and the decay rate of the resonator $\kappa$ are derived, assuring distinct vacuum Rabi oscillation in a strong coupling regime [$(g,\gamma ,\kappa )\approx (30,25,8.0)\mathrm{MHz}$]. The magnitude of decoherence is consistently interpreted in terms of the coupling of electrons to piezoelectric acoustic phonons in GaAs.

Figure 1

(a) Optical microscope image of the coupled DQD-CPW resonator system. The location the where DQD is coupled is marked by the red square, the blown up version of which is shown in (b). (c) It is a scanning electron microscope image of the DQD, defined by biasing metal ($\mathrm{NiCr}/\mathrm{Au}$) gates GL (left), GC (center), and GR (right). The right QD is capacitively coupled ($C_r\approx 50\mathrm{aF}$) with gate electrode Gr to the resonator. (d) Equivalent circuit of the device. The two QDs are designed to be nominally equal, except in the presence of Gr. The resonator is weakly coupled at opposite ends to the transmission line through $C_c=3\mathrm{fF}$.

Figure 2

Charge stability diagram of the DQD represented on the plane of $V_L$ and $V_R$, where $V_C=-215\mathrm{mV}$. (a) dc conductance through the DQD, (b) the transmission amplitude, and (c) the phase of the CPW resonator. The microwave frequency is fixed at 8.3267 GHz.

Figure 3

(a) The DQD conductance and (b) the resonator transmission amplitude at 8.3267 GHz in the vicinity of charge triple points, with $V_C=-200\mathrm{mV}$.

Figure 4

(a) Transmission spectra of the resonator as a function of interdot energy difference $ϵ$. $V_L$ and $V_R$ are scanned along the dashed red line in Fig. 3b. The gate voltages are converted to the energy difference in frequency units using a conversion constant derived from PAT measurements [20]. (b) The peak position and (c) the linewidth of the transmission spectra. The solid red (dashed green) curve in (b) indicates theoretical values [Eq. (2)], with $g/2\pi =20(30)\mathrm{MHz}$. (d) Energy diagram of the DQD (thin dashed red curve, $|e,0⟩$), the resonator (horizontal dotted blue line, $|g,1⟩$) and the coupled system (solid green curves, $|\pm ⟩$). The corresponding quantum states are denoted by the respective colors.