Dispersive Readout of a Few-Electron Double Quantum Dot with Fast rf Gate Sensors

We report the dispersive charge-state readout of a double quantum dot in the few-electron regime using the in situ gate electrodes as sensitive detectors. We benchmark this gate sensing technique against the well established quantum point contact charge detector and find comparable performance with a bandwidth of $\sim 10\mathrm{MHz}$ and an equivalent charge sensitivity of $\sim 6.3\times {10}^{-3}e/\sqrt{\mathrm{Hz}}$. Dispersive gate sensing alleviates the burden of separate charge detectors for quantum dot systems and promises to enable readout of qubits in scaled-up arrays.

Figure 1

(a) Micrograph of a similar device to the one measured and circuit schematic. One of the in situ dot-defining gates (blue) is coupled via a bondwire to an off-chip $\mathrm{Nb}/{\mathrm{Al}}_2{\mathrm{O}}_3$ superconducting lumped-element resonator to enable dispersive readout. (b) Amplitude ${\mathrm{S}}_{11}$ (blue or dark grey) and phase response (red or light grey) of the resonator. (c) Illustration of the charging energy spectrum for a quantum dot. The resonant rf gate voltage $V_{\mathrm{rf}}$ induces tunneling at the charge degeneracy point (green oscillation) leading to a dispersive shift that is suppressed for configurations of stable charge (orange oscillation).

Figure 2

(a) Dispersive signal from the gate sensor showing transitions in electron number for a large single quantum dot. Green (square) and orange (hex) symbols correspond to positions of symbols in Fig. 1c. (b) Derivative of the QPC conductance signal with gate voltage $V_{g}L$ in a region of gate space similar to (a). The slight shift in gate voltage and period of the oscillations in comparison to (a) is due to the presence of the QPC gate bias. (c) Phase response of the gate sensor showing peaks corresponding to single electron transitions. (d) Vertical slice through the conductance signal in (b), at $V_{g}R=-723\mathrm{mV}$. (e) SNR of the gate sensor as a function of the modulation frequency of a signal applied to a nearby gate. (f) SNR for the gate sensor as a function of carrier frequency. (g) Width and height of the DGS response signal with power applied to the resonator (before $\sim 44\mathrm{dB}$ of attenuation). (h) Coulomb charging diamonds for the quantum dot, measured using the gate sensor in a regime where direct transport is not possible. Color scale is the derivative of the dispersive signal. Labels indicate number of electrons.

Figure 3

(a) Dispersive response $V_{\mathrm{DGS}}$ from the gate sensor for a few-electron double quantum dot. Labels indicate number of electrons in the left and right dot. (b) Equivalent charge sensing signal from the QPC detector confirming the few-electron regime. The shift in location of the transitions compared to the data in (a) is due to the required QPC gate bias. (c) Temperature dependence of the sensing signal for both the DGS (left axis, solid line data) and QPC (right axis, dashed line data). The transitions are taken at a fixed $V_{g}R$ and offset vertically for clarity. Both detectors resolve clear sensing peaks at $T\sim 20\mathrm{mK}$, with the QPC losing all sensitivity at elevated temperature $T\sim 1100\mathrm{mK}$. (d) DGS signal in a zoomed-up region showing a double dot charge transition. (e) The calibrated phase response from the DGS for a slice through (d) with $V_{g}R$ held at $-608\mathrm{mV}$. (f) Dispersive response of the gate sensor where tunneling to the reservoirs is suppressed in the few-electron limit. High tunnel rate, intradot transitions remain visible.