Charge reconfiguration in arrays of quantum dots

Semiconductor quantum dots are potential building blocks for scalable qubit architectures. Efficient control over the exchange interaction and the possibility of coherently manipulating electron states are essential ingredients towards this goal. We studied experimentally the shuttling of electrons trapped in serial quantum dot arrays isolated from the reservoirs. The isolation hereby enables a high degree of control over the tunnel couplings between the quantum dots, while electrons can be transferred through the array by gate voltage variations. Model calculations are compared with our experimental results for double, triple, and quadruple quantum dot arrays. We are able to identify all transitions observed in our experiments, including cotunneling transitions between distant quantum dots. The shuttling of individual electrons between quantum dots along chosen paths is demonstrated.

Figure 1

False color SEM image of the QQD device; the QDs are depicted as green circles. All measurements shown are performed using the QPC charge detector defined by Qg1. As indicated by the red arrows, electrons can be shifted through the QD system by gate voltage variations.

Figure 2

(a) DQD stability diagram as a function of $V_{Tg2}$ and $V_{Tg4}$. Red dashed lines represent the isolation threshold, where tunneling rates through the respective barrier drop below the measurement frequency. (b) Calculated capacitive model stability diagram. (c) Scheme of the DQD setup. Light blue gates are at fixed voltages, dark blue gates are varied for the measurement, and white gates are grounded. Only the reddish colored DQD is defined. (d)–(f) Energy level schemes of the three points marked in (a) and (b). Panel (d) marks the $(2,0)\to (1,1)$ transition, (e) the resonance between the lowest level of both QDs, and (f) the $(1,1)\to (0,2)$ transition.

Figure 3

(a) Isolated TQD stability diagram as a function of $V_{Dg1}$ and $V_{Dg3}$ with inset sample scheme similar to Fig. 2. Sequential transitions are marked in green/orange; the cotunneling transition $(1\to 3)$ is marked in red. Points A and B mark two TQD resonances occurring for identical charge configurations at the isolation point. (b) Capacitive model simulations excluding and (c) including transitions directly from QD1 to QD3. Transitions marked as in (a). (d) Scheme of cotunneling transitions directly between both outer QDs via two different virtual states of the detuned center QD. (e) Scheme of a TQD resonance in the isolated region. (f) Zoom into simulated resonances, allowing the distinction between resonances occupied by one (top) or two electrons (bottom).

Figure 4

(a) Isolated QQD stability diagram as a function of $V_{Dg1}$ and $V_{Dg4}$ with inset sample scheme. Transitions are marked according to the simulation. (b) Capacitive model simulation of an isolated QQD stability diagram. One of each of the six possible transitions is marked by an ellipse.