L- and C-SET


Owing to the limitations due to the dissipative nature of the rf-SET, we have been developing an inductive read-out technique for a superconducting SET, called the L-SET (Inductive SET). With zero DC-voltage, a superconducting SET (SSET) behaves as an energy-storing reactive component because of the Josephson coupling. Tuning the gate charge changes the effective inductance of the SSET between the drain and the source. This effect is used to tune the resonance frequency of a resonator in the L-SET configuration.

We consider the L-SET the most promising method of sensitive and fast electrometry. In addition, since its operation is based on correlated supercurrent, the back action noise of a L-SET is clearly less than that of a regular SET. Energy sensitivity of hbar appears to be within reach using rather standard rf-techniques.

Charge sensitivity 3x10-5 e/√Hz, limited by preamplifier, has been achieved in an operation mode which takes advantage of the nonlinearity of the Josephson potential. Owing to reactive readout, our setup has more than two orders of magnitude lower dissipation than the existing method of radio-frequency electrometry.

Principle of the L-SET measurement. In the L-SET circuit, the plasma frequency in a superconducting SET (SSET) is tuned below one GHz by a parallel LC circuit. Since the Josephson inductance of the SSET has a substantial gate charge dependence, resonant frequency of the whole circuit is gate-dependent (in linear regime).
Frequency response is measured by continuous-wave microwave irradiation. The microwave reflection coefficient Gamma shows the effect of tuning of the SSET Josephson inductance.
Measured frequency response of the L-SET circuit plotted as a function of strength of the microwave irradiation. When the drive exceeds the regime of linear oscillations at a critical power PC, resonance frequency shifts abruptly. This can be seen as an analogue of a DC-biased junction switching into voltage state.

Related publications

  • Charge sensitivity of the inductive single-electron transistor

M.A. Sillanpää, L. Roschier, P.J. Hakonen

Appl. Phys. Lett. 87, 092502 (2005)

  • Inductive single-electron transistor

M.A. Sillanpää, L. Roschier, and P.J. Hakonen

Phys. Rev. Lett. 93, 066805 (2004)


Capacitive SET is the dual circuit of the L-SET. Instead of the second derivative with respect to phase, that is used to obtain a charge-dependent inductance in L-SET, the C-SET operation employs the second derivative with respect to gate charge which yields a phase-dependent capacitance.

Unlike any previous considerations of single-electron or single Cooper-pair devices, implementation of the C-SET device is a generally fast and sensitive phase detector. The sensitivity is estimated to to 30x10-6 rad/√Hz for typical HEMT preamplifiers with a noise temperature of 3 K.

Schematics of the C-SET circuitry. Variation of the quantum capacitance of the SSET changes the resonant frequency of LC-matching circuit, which can be read out from the phase of the reflected signal.

Related publications

  • Direct observation of Josephson capacitance

M.A. Sillanpää, T. Lehtinen, A. Paila, Yu. Makhlin, L. Roschier, and P.J. Hakonen

Phys. Rev. Lett. 95, 206806 (2005)