Charge sensing of an artificial ${\mathrm{H}}_2^{+}$ molecule in lateral quantum dots

We report charge detection studies of a lateral double quantum dot with controllable charge states and tunable tunnel coupling. Using an integrated electrometer, we characterize the equilibrium state of a single electron trapped in the double-dot (artificial ${\mathrm{H}}_2^{+}$ molecule) by measuring the average occupation of one dot. We present a model where the electrostatic coupling between the molecule and the sensor is taken into account explicitly. From the measurements, we extract the temperature of the isolated electron and the tunnel coupling energy. It is found that this coupling can be tuned between 0 and $60\mu \mathrm{eV}$ in our device.

Figure 1

(a) SEM picture of the experimental device. Scale bar: 500 nm; (b) Schematic representation of the different regions shaped by the gates in the 2DEG. Dots 1 and 2 are connected in series to the leads labeled “source” and “drain” by tunneling barriers. The double arrows indicate where particle exchange can occur. The QPC current $I_{\mathrm{QPC}}$ flows through a constriction closest to dot 2. Charge sensing is performed by monitoring the transconductance $d{I}_{\mathrm{QPC}}∕d{V}_{2\mathrm{B}}$; (c) Stability diagram of the double quantum dot obtained by charge sensing. The electron number for each dot is indicated by $(N_1,N_2)$. The background signal was subtracted for clarity.

Figure 2

(a) Transconductance map near the transition (1,0) to (0,1) for $V_{3\mathrm{B}}=-0.31\mathrm{V}$; (b) Experimental stability diagram. The positions of the resonances A, B, and C from (a) are plotted (open circles). The spacing $\Delta$ between triple points $\alpha$ and $\beta$ is equal to $2t+\gamma$. The scale bars are equal to $300\mu \mathrm{eV}$; (c) Average occupation, $M$, of dot 2 as a function of the detuning energy $ϵ$ calculated using Eq. (2a, 2b, 2c) for several values of the back-action parameter $y$. ${\Gamma }_r,T_e$, and $t$ equal 0.26, 6, and $7\mu \mathrm{eV}$ for this plot. Inset: Numerical derivative of $M$ with respect to $ϵ$ of the same curves.

Figure 3

Temperature dependence of the $dM∕dϵ$ peak along the detuning line, $V_{3\mathrm{B}}=-0.31\mathrm{V}$. For each trace, the dilution refrigerator and electronic temperature $(T,T_e)$ are indicated in mK. The solid lines are fit of Eq. (2a, 2b, 2c) to the data points assuming $t=7\mu \mathrm{eV}$ and $y=0$. Traces are shifted vertically. Inset: $T_e$ extracted from the fits plotted as a function of $T$. The line $T_e=T$ is also shown (dashed).

Figure 4

(a) Experimental stability diagram obtained for three different values of gate voltage $V_{3\mathrm{B}}$; (b) Dependance of the $dM∕dϵ$ peak with gate voltage. For each trace, the gate voltage and the tunnel coupling $(V_{3\mathrm{B}},t)$ are indicated in V and $\mu \mathrm{eV}$ respectively. The solid lines are fit to the data assuming $T_e=78\mathrm{mK}$ and $y=0$. Traces are shifted vertically. Inset: $2t\text{vs}{V}_{3\mathrm{B}}$ extracted from the fits.