Schematic of the twin rf-SET setup. Signals are coupled to the tank circuits by using a directional coupler and are then directed to the corresponding SET by the tuned impedance transformers. The reflected signal feeds cryogenic and room temperature amplifiers. Two bias tees allow independent dc-biasing of each SET. Shaded region: Schematic of the rf carrier generation and signal demodulation. The incident carrier wave is produced by combining the output of two independent rf signal generators. The bottom section shows a SEM image of a twin-SET device. The tunnel barriers required for Coulomb blockade are formed after the first evaporation step by in situ oxidation of the aluminum surface. For SET2 (right) the overlaps of source and drain leads (second evaporation) with the SET island (first evaporation) can be seen.
(a) and (b) Lumped element calculations of the power reflection coefficient as a function of the SET resistance for impedance transformers designed to match to for (a) and to for (b). The shaded regions correspond to the matching regimes shown in (c) and (d). (c) Reflected rf power (top, ) and dc conductance (bottom) in the superconducting state. The SET resistance remains above (note the different scale on the axis) throughout and the impedance transformer operates in the under matched regime. (d) Reflected rf power (top, ) and dc conductance (bottom) with the SET biased to a region where the resistance at the top of a peak is less than . The nonmonotonic dependence on gate bias arises as the operating point moves from under to over matched.
Simulation results (Ref. 18) showing the effect of shunt stub tuning. (a) Shows the ideal case where crosstalk is kept to a minimum ( and ). As indicated by the inset, at is hardly effected by varying the resistance of SET1, only varying slightly in the overmatched case. Contrasting this behavior (b) shows simulation results for an unoptimized stub network. In this scenario the cross talk between the two tank circuit is near 50% despite the increased factor. For clarity the linear is shown.
Comparison between simulation results and experimental data. For the experimental data , , , , , and varies from (top) to (bottom). We adjust the lengths of the stub network and the length of the bond wires linking the chip to the circuit board as fitting parameters. Small deviations between the simulation results and experiment are most likely due to the input impedance of the cryogenic amplifier, which deviates from across the frequency span.
(a) Typical AM signal associated with both the SETs responding to a , gate signal. Charge sensitivities for each device are stated for the case of simultaneous operation (different measurement). (b) Time domain data taken simultaneously with both SETs. Both devices respond independently to a square wave signal applied to a nearby gate. Spurious charge noise is superimposed on the output of SET2 (shown in the hashed region). By cross correlating the signals from both SETs (multiplying the derivatives) we are able to suppress spurious charge noise events in real time.
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