Fast sensing of double-dot charge arrangement and spin state with a radio-frequency sensor quantum dot

Single-shot measurement of the charge arrangement and spin state of a double quantum dot are reported with measurement times down to 100 ns. Sensing uses radio-frequency reflectometry of a proximal quantum dot in the Coulomb blockade regime. The sensor quantum dot is up to 30 times more sensitive than a comparable quantum point-contact sensor and yields three times greater signal to noise in rf single-shot measurements. Numerical modeling is qualitatively consistent with experiment and shows that the improved sensitivity of the sensor quantum dot results from reduced lifetime broadening and screening.

Figure 1

(Color online) (a) Micrograph of lithographically identical device. Gate voltages $V_{\text{L}}$ and $V_{\text{R}}$ control the double-dot charge state $\left(N_{\text{L}},N_{\text{R}}\right)$ (see Fig. 2). Quantum point-contact QPC1 (blue, dashed) controlled by gate voltage $V_{\text{Q}1}$, SQD (red, solid) and by plunger gate $V_{\text{D}}$ can also be operated as a point contact (QPC2) (black, solid) apply gate voltage $V_{\text{Q}2}$ to the bottom gate with top two grounded. QPC1(2) and SQD measured by dc transport in first device. SQD measured by rf reflectometry in subsequent cooldown of second identical device. (b) dc conductance, $g$, of QPC1,2 (left scale) and SQD (right scale) as a function of gate voltage changes $\Delta V_{\text{D}}$, $\Delta V_{\text{Q}1}$, and $\Delta V_{\text{Q}2}$.

Figure 2

(Color online) (a) SQD dc conductance $g$ as a function of voltages $V_{\text{L}}$ and $V_{\text{R}}$, with charge occupancy $\left(N_{\text{L}},N_{\text{R}}\right)$ indicated. Note the large relative change in conductance, $\Delta g/\overline{g}\sim 0.9$ as double dot switches from (0,2) to (1,1). (b) QPC2 conductance shows a small $\left(\Delta g/\overline{g}\sim 3\mathrm{\%}\right)$ change as the dot switches from (0,2) to (1,1). A similar value is seen for QPC1 (not shown). [(c) and (d)] Cuts through (a) and (b), respectively. All data are for device 1.

Figure 3

(Color online) (a) Probability density $P$ of single-shot outcomes, $V_{\text{rf}}$, (0.7 mV binning) as a function of integration time, ${\tau }_{\text{M}}$, of the rf-charge signal $v_{\text{rf}}$ (Ref. 12). Measured with SQD, device 2. The left [right] peak corresponds to the (0,2) [(1,1)] charge state and therefore singlet [triplet] measurement outcomes (Ref. 5). (b) Cuts of $V_{\text{rf}}$ along the dashed lines in (a) along with theoretical curves (Ref. 5). (c) SNR, defined as peak separation $\Delta V$ divided by peak width $\sigma$ as a function of measurement integration time ${\tau }_{\text{M}}$ for QPC1 (device 1, $-89\text{dBm}$ rf power) and SQD (device 2, $-99\text{dBm}$ rf power), along with theory curves (see text).

Figure 4

(Color online) (a) Conductance (simulation) through the SQD as function of the gate voltage $V_{\text{D}}$, for the two double-dot charge states (1,1) and (0,2). (b) Conductance through QPC1 at 5 mV intervals (lines are guide to the eye). (c) Electron density profile for typical gate voltages in the (1,1) configuration, with superimposed micrograph of device. The color scale is centered near $2.5\times {10}^{10}{\text{cm}}^{-2}$ to accentuate the charge in the dots and the saddle point of QPC1.