Microwave-Driven Transitions in Two Coupled Semiconductor Charge Qubits

We have studied interactions between two capacitively coupled $\mathrm{GaAs}/\mathrm{AlGaAs}$ few-electron double quantum dots. Each double quantum dot defines a tunable two-level system, or qubit, in which a single excess electron occupies the ground state of either one dot or the other. Applying microwave radiation, we resonantly drive transitions between states and noninvasively measure occupancy changes using proximal quantum point contact charge detectors. The level structure of the interacting two-qubit system is probed by driving it at a fixed microwave frequency while varying the energy detuning of both double dots. We observe additional resonant transitions consistent with a simple coupled two-qubit Hamiltonian model.

Figure 1

(a) Scanning electron micrograph of a control sample showing the gate pattern for the device measured. (b) Measured charge stability diagram for the top double dot showing the top QPC conductance $g_1$ against $V_{R1}$ and $V_{L1}$. (c) Measured charge stability diagram for the bottom double dot showing $g_2$ against $V_{R2}$ and $V_{L2}$. For both (b) and (c), planes have been subtracted from the data to compensate for gate coupling. (d) One-half of the resonant microwave splitting against microwave frequency for the top (circles) and bottom (triangles) double dots. The solid lines are least-square fits to theory with the $x$-axis intercept giving $2t_i$. We vary $t_i$ by adjusting $V_{Mi}$.

Figure 2

(a) and (b) plot the top and bottom charge sensing signals, respectively, against $V_{L1}$ and $V_{L2}$ showing the diagonal region where the two double dots interact. To account for charge detector drift in (a) we sweep $V_{L1}$ and step $V_{L2}$, while in (b) we sweep $V_{L2}$ and step $V_{L1}$. Each data trace has also had an offset and slope subtracted from it.

Figure 3

(a) We repeat the measurement in Fig. 2a with a 20 GHz continuous wave signal applied. For clarity we differentiate the data with lighter regions indicating high $d{g}_1/d{V}_{L1}$. (b)–(d) We show the detector signal traces along the dashed lines marked (i)–(iii), respectively, in (a). We also plot the corresponding calculated band structure with arrows showing how the observed resonances coincide with 20 GHz energy gaps between the ground state and excited states. The approximate eigenstates are indicated in the form $|LR⟩\equiv |L_1⟩|R_2⟩$.

Figure 4

(a) The same as Fig. 3a but with the modeled resonances for transitions to the three excited states overlaid. The arrows indicate two photon events as described in the text. (b) We repeat (a) but with a 11 GHz continuous wave signal applied. (c) Similar to (a) but with weaker coupling in the bottom double dot. In (a)–(c), lighter regions indicate high $d{g}_1/d{V}_{L1}$. (d) Both the top and bottom detector signals along the solid line marked in (c). The expected transition positions are indicated by the arrows.