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Superconducting Electrometer Based on the Resistively Shunted Bloch Transistor

S. V. Lotkhov, H. Zangerle, Alexander B Zorin, Thomas Weimann, Hansjorg Scherer, J. Niemeyer

Published Jan 1, 1999• 2 citations
OpenAlex

Abstract

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 The Bloch transistor normally consists of two small Josephson junctions connected in series, which in our case have been replaced by two superconducting interferometer loops, each with two junctions in parallel.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

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 The Bloch transistor normally consists of two small Josephson junctions connected in series, which in our case have been replaced by two superconducting interferometer loops, each with two junctions in parallel.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

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Nicolas Boulant, Grégoire Ithier, François Nguyen +5 more

Bloch oscillations predicted to occur in current-biased single Josephson junctions have eluded direct observation up to now. Here, we demonstrate similar Bloch oscillations in a slightly richer Josephson circuit, the quantronium. The quantronium is a Bloch transistor with two small junctions in series, defining an island, in parallel with a larger junction. In the ground state, the microwave impedance of the device is modulated periodically with the charge on the gate capacitor coupled to the transistor island. When a current flows across this capacitor, the impedance modulation occurs at the Bloch frequency, which yields Bloch sidebands in the spectrum of a reflected continuous microwave signal. We have measured this spectrum, and compared it to predictions based on a simple model for the circuit. We discuss the interest of this experiment for metrology and for mesoscopic physics.

arXiv:cond-mat/0605061•May 2, 2006•0 citations
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 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 propose a superconducting circuit based on the Bloch transistor, a quantum device consisting of two small-capacitance Josephson junctions, connected in series and having a small superconducting island in between. This device is driven by two dc electrical sources controlling Josephson oscillations of frequency fJ=2eVJ‾/hf_J = 2e\overline{V_J}/hfJ​=2eVJ​​/h, related to the average transistor voltage VJ‾\overline{V_J}VJ​​, and Bloch oscillations of frequency fB=IB‾/2ef_B = \overline{I_B}/2efB​=IB​​/2e, related to the average current IB‾\overline{I_B}IB​​ injected into the transistor island. We show that due to the Bloch transistor properties, these two types of oscillations are coupled and can mutually phase-lock, i.e., fJ=fBf_J = f_BfJ​=fB​. This leads to the formation of a current step on the current-voltage curve at IB‾=2efJ\overline{I_B} = 2ef_JIB​​=2efJ​, which is similar to the dual Shapiro step, appearing under microwave irradiation of frequency fff on the current-voltage curve of a small Josephson Junction at current I=2efI=2efI=2ef. Moreover, the Bloch transistor transconductance IB‾/VJ‾\overline{I_B}/\overline{V_J}IB​​/VJ​​ takes the fundamental value of 1/RQ1/R_Q1/RQ​, where RQ=h/4e2R_Q = h/4e^2RQ​=h/4e2 is the resistance quantum. The obtained results pave the way to an alternative quantum standard of resistance, based on the superconducting circuit and operating without applying a strong magnetic field.
In a system where two small-area (100 nm x 100 nm) superconducting tunnel junctions are connected in series, the Josephson effect which tends to impose the phase competes with the charging effects in the central electrode (the "island" of the device) which tend to set the charge of the island. By applying a voltage on an electrode capacitively coupled to the island (the "gate" electrode) one can arbitrate this competition in favour of either effect. This is can be seen in particular on the supercurrent which can flow through the junctions : it is modulated periodically by the gate voltage (hence the name of "transistor" given to the system). This modulation shows sharp peaks when two charge states of the island are degenerate with respect to the electrostatic energy. The system is then in a state which has no classical description : it is in a coherent superposition of states. In this thesis we demonstrate experimentally the behaviour of this transistor and we analyse the theoretical and practical problems which can prevent the observation of the coherent superposition of states through the modulation of the supercurrent. In particular we show that the parity of the electron number in the island must be rigorously controlled and that the impedance connected to the circuit plays a crucial role in setting the magnitude of the measured supercurrent.
Bloch oscillations predicted to occur in current-biased single Josephson junctions have eluded direct observation up to now. Here, we demonstrate similar Bloch oscillations in a slightly richer Josephson circuit, the quantronium. The quantronium is a Bloch transistor with two small junctions in series, defining an island, in parallel with a larger junction. In the ground state, the microwave impedance of the device is modulated periodically with the charge on the gate capacitor coupled to the transistor island. When a current flows across this capacitor, the impedance modulation occurs at the Bloch frequency , which yields Bloch sidebands in the spectrum of a reflected continuous microwave signal. We have measured this spectrum, and compared it to predictions based on a simple model for the circuit. We discuss the interest of this experiment for metrology and for mesoscopic physics.
In a system where two small-area (100 nm x 100 nm) superconducting tunnel junctions are connected in series, the Josephson effect which tends to impose the phase competes with the charging effects in the central electrode (the of the device) which tend to set the charge of the island. By applying a voltage on an electrode capacitively coupled to the island (the electrode) one can arbitrate this competition in favour of either effect. This is can be seen in particular on the supercurrent which can flow through the junctions : it is modulated periodically by the gate voltage (hence the name of given to the system). This modulation shows sharp peaks when two charge states of the island are degenerate with respect to the electrostatic energy. The system is then in a state which has no classical description : it is in a coherent superposition of states. In this thesis we demonstrate experimentally the behaviour of this transistor and we analyse the theoretical and practical problems which can prevent the observation of the coherent superposition of states through the modulation of the supercurrent. In particular we show that the parity of the electron number in the island must be rigorously controlled and that the impedance connected to the circuit plays a crucial role in setting the magnitude of the measured supercurrent.
Bloch oscillations predicted to occur in current-biased single Josephson junctions have eluded direct observation up to now. Here, we demonstrate similar Bloch oscillations in a slightly richer Josephson circuit, the quantronium. The quantronium is a Bloch transistor with two small junctions in series, defining an island, in parallel with a larger junction. In the ground state, the microwave impedance of the device is modulated periodically with the charge on the gate capacitor coupled to the transistor island. When a current flows across this capacitor, the impedance modulation occurs at the Bloch frequency, which yields Bloch sidebands in the spectrum of a reflected continuous microwave signal. We have measured this spectrum, and compared it to predictions based on a simple model for the circuit. We discuss the interest of this experiment for metrology and for mesoscopic physics.