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IEEE Transactions on Instrumentation and Measurement

Ultimate sensitivity of the single Cooper pair tunneling electrometer

Alexander B Zorin

Published Apr 1, 1997• 11 citations
Publisher

Abstract

The small capacitance superconducting two-junction structure shunted as a whole by a small-size resistor has been theoretically studied. When the bias current slightly exceeds the critical current of the system, the nonzero average voltage on the resistor and its response to small variations of the polarization charge Q/sub 0/ on the common electrode appear. The sensitivity of such an electrometer has been optimized.

DOI
10.1109/19.571838

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physica status solidi (b)•Feb 1, 1996•0 citations
The small capacitance superconducting two-junction structure shunted as a whole by a small-size resistor has been theoretically studied. When the bias current slightly exceeds the critical current of the system, the nonzero average voltage on the resistor and its response to small variations of the polarization charge Q/sub 0/ on the common electrode appear. The sensitivity of such an electrometer has been optimized.
We propose a system comprising the small-capacitance double Josephson junction shunted as a whole by a small resistance $({R}_{S}\ensuremath{\ll}{R}_{Q}\ensuremath{\equiv}{h/4e}^{2})$. We have calculated the dynamic and noise characteristics of the system as functions of a polarization charge on the central electrode. It has been shown straightforwardly that the energy resolution of such an electrometer implying the ``backaction noise'' approaches the fundamental quantum limit $\ensuremath{\Elzxh}/2$ when $T\ensuremath{\rightarrow}0$.
We have fabricated the Bloch transistor shunted on-chip by a small-sized Cr resistor with R/sub s/=1 k/spl Omega/. The Bloch transistor normally consists of two small Josephson junctions connected in series, which in our case have been replaced by two superconducting interferometer loops, each with two junctions in parallel. A capacitively coupled gate is supplied to control the induced charge of the small intermediate electrode (island) of the transistor. The measured I-V curves show no hysteresis and correspond to the operation of a effective Josephson junction at the high-damping and strong-noise limits. The critical current of the system was found to be close to its nominal value, that is in accordance with the electromagnetic environment theory. The I-V curves were modulated by the gate with a period of e and a maximum swing of about 2 /spl mu/V. Such rather moderate modulation results from the Josephson-to-charging energies ratio, E/sub J//E/sub C//spl ap/9, in our sample being far from its optimum value (/spl ap/0.3+1).
Abstract⎯We have fabricated the Bloch transistor shunted on-chip by a small-sized Cr resistor with Rs ≈ 1 kΩ. The Bloch transistor normally consists of two small Josephson junctions connected in series, which in our case have been replaced by two superconducting interferometer loops, each with two junctions in parallel. A capacitively coupled gate is supplied to control the induced charge of the small intermediate electrode (island) of the transistor. The measured I-V curves show no hysteresis and correspond to the operation of a effective Josephson junction at the high-damping and strong-noise limits. The critical current of the system was found to be close to its nominal value, that is in accordance with the electromagnetic environment theory. The I-V curves were modulated by the gate with a period of e and a maximum swing of about 2 µV. Such rather moderate modulation results from the Josephson-tocharging energies ratio, EJ/EC ≈ 9, in our sample being far from its optimum value ( ≈ 0.3÷1). I.
We have measured the current-voltage $(I\ensuremath{-}V)$ characteristics of small-capacitance single Josephson junctions at low temperatures (T=0.02−−0.6K),(T=0.02--0.6\mathrm{K}),(T=0.02−−0.6K), where the strength of the coupling between the single junction and the electromagnetic environment was controlled with one-dimensional arrays of dc superconducting quantum interence devices (SQUIDs). The single-junction $I\ensuremath{-}V$ curve is sensitive to the impedance of the environment, which can be tuned in situ. We have observed Coulomb blockade of Cooper-pair tunneling and even a region of negative differential resistance, where the zero-bias resistance ${R}_{0}^{\ensuremath{'}}$ of the SQUID arrays is much higher than the quantum resistance ${R}_{K}\ensuremath{\equiv}{h/e}^{2}\ensuremath{\approx}26\mathrm{k}\ensuremath{\Omega}.$ The negative differential resistance is evidence of the coherent single-Cooper-pair tunneling within the theory of current-biased single Josephson junctions. Based on this theory, we have calculated the $I\ensuremath{-}V$ curves numerically in order to compare then with the experimental ones at ${R}_{0}^{\ensuremath{'}}\ensuremath{\gg}{R}_{K}.$ The numerical calculation agrees with the experiments qualitatively. We also discuss the ${R}_{0}^{\ensuremath{'}}$ dependence of the single-Josephson-junction $I\ensuremath{-}V$ curve in terms of the superconductor-insulator transition driven by changing the coupling to the environment.
Assuming the absence of 1/f noise, we have calculated the charge sensitivity (CS) of a capacitive-coupled double-junction single electron tunneling transistor (SETT) with a superconducting grain, operating at low temperature and low bias voltage such that the tunneling current is dominated by the Andreev process. In this case the effect of co-tunneling is suppressed without using the complicated fabrication method. We have used a realistic sample to demonstrate the procedure of optimizing the CS of a SETT with respect to relevant physical parameters and structure parameters. With the presently available fabrication technology, our theoretical analysis can serve as a guide for increasing the CS of a SETT beyond 10−6 e/√Hz.
Abstract Single‐charge tunneling through a voltage‐biased SSS transistor with a capacitively coupled gate and an electromagnetic environment is considered. The dc Cooper‐pair current in the blockade region of quasiparticle tunneling is studied. Basing on a two‐level approximation, which can be used in the realistic case of low temperatures and small environment resistances, the mean dc Cooperpair current, the noise power spectrum, and the charge resolution are calculated as functions of the driving voltage and the external charge on the island.