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Physical Review Letters

Quantum-Limited Electrometer Based on Single Cooper Pair Tunneling

Alexander B Zorin

Published Jun 3, 1996• 82 citations
Publisher

Abstract

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 $T\ensuremath{\rightarrow}0$.

DOI
10.1103/physrevlett.76.4408

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S. V. Lotkhov, H. Zangerle, Alexander B Zorin +3 more

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 The Bloch transistor normally consists of two small Josephson junctions connected in series, which in our case have been replaced by two superconducting interferometer loops, each with two junctions in parallel.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.

•Jan 1, 1999•2 citations
We propose a system comprising the small-capacitance double Josephson junction shunted as a whole by a small resistance (RS\ensuremath≪RQ\ensuremath≡h/4e2)({R}_{S}\ensuremath{\ll}{R}_{Q}\ensuremath{\equiv}{h/4e}^{2})(RS​\ensuremath≪RQ​\ensuremath≡h/4e2). 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\ensuremath{\Elzxh}/2\ensuremath\Elzxh/2 when T\ensuremath→0T\ensuremath{\rightarrow}0T\ensuremath→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).
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.
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.
We study the quantum charge noise and measurement properties of the double Cooper-pair resonance point in a superconducting single-electron transistor (SSET) coupled to a Josephson charge qubit. Using a density-matrix approach for the coupled system, we obtain a full description of the measurement backaction; for weak coupling, this is used to extract the quantum charge noise. Unlike the case of a nonsuperconducting SET, the backaction here can induce population inversion in the qubit. We find that the Cooper-pair resonance process allows for a much better measurement than a similar nonsuperconducting SET, and can approach the quantum limit of efficiency.
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.