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Science

Low-Noise Current Amplifier Based on Mesoscopic Josephson Junction

Julien Delahaye, Juha Hassel, Rene K. Lindell, Mika A. Sillanpää, Mikko A. Paalanen, Heikki Seppä, Pertti Juhani Hakonen

Published Feb 13, 2003• 64 citations
Publisher

Abstract

We used the band structure of a mesoscopic Josephson junction to construct low-noise amplifiers. By taking advantage of the quantum dynamics of a Josephson junction, i.e., the interplay of interlevel transitions and the Coulomb blockade of Cooper pairs, we created transistor-like devices, Bloch oscillating transistors, with considerable current gain and high-input impedance. In these transistors, the correlated supercurrent of Cooper pairs is controlled by a small base current made up of single electrons. Our devices reached current and power gains on the order of 30 and 5, respectively. The noise temperature was estimated to be around 1 kelvin, but noise temperatures of less than 0.1 kelvin can be realistically achieved. These devices provide quantum-electronic building blocks that will be useful at low temperatures in low-noise circuit applications with an intermediate impedance level.

DOI
10.1126/science.299.5609.1045

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We used the band structure of a mesoscopic Josephson junction to construct low-noise amplifiers. By taking advantage of the quantum dynamics of a Josephson junction, i.e., the interplay of interlevel transitions and the Coulomb blockade of Cooper pairs, we created transistor-like devices, Bloch oscillating transistors, with considerable current gain and high-input impedance. In these transistors, the correlated supercurrent of Cooper pairs is controlled by a small base current made up of single electrons. Our devices reached current and power gains on the order of 30 and 5, respectively. The noise temperature was estimated to be around 1 kelvin, but noise temperatures of less than 0.1 kelvin can be realistically achieved. These devices provide quantum-electronic building blocks that will be useful at low temperatures in low-noise circuit applications with an intermediate impedance level.
This thesis is a compilation of several works in the area of condensed matter physics, and with devices based on superconducting Josephson junctions (JJ) as the common denominator for the presented projects apart from the work on diffusive systems. Microwave measurements were conducted on a Superconducting Cooper pair transistor to explore its current-phase relationship. Measurements on a JJ-based qubit coupled to a LC resonator revealed the vibronic transitions obeying the Franck-Condon principle. The main body of the thesis is the work done on the Bloch Oscillating Transistor (BOT), an ultra low noise quantum amplifier. In the present work, we investigated the dynamics of the BOT near the bifurcation threshold as well as implemented differential BOTs to check its capability to reject common mode signals. To account for our studies of quantum features in mesoscopic systems other than JJs, we performed an experiment similar to the Hanbury-Brown and Twiss interferometry in optics. For this mesoscopic interference experiment we selected a multiterminal diffusive system. We developed a low temperature noise measurement scheme to study current-current correlations in the GHz frequency range. In our experiments we found a small positive HBT exchange correction factor in the non-interacting limit at low bias voltage in the presence of quantum interference. We found negative exchange correction factor in the hot electron case for similar structures, which agrees well with the theory. Altogether, our experiments demonstrated the theoretically predicted HBT exchange effects in non-interacting and interacting regime of electron transport in a diffusive mesoscopic system.
This thesis work deals with a range of superconducting devices operated near the fundamental performance limits set by quantum mechanics along with the nature of quantum vacuum itself when perturbed by such devices. These devices are operated in a dilution refrigerator cooled down to sub-Kelvin temperatures. Low temperature is absolutely essential for quantum behavior of these devices and the minimal inherent noise contribution. Biased, selectively damped superconducting tunnel junction, (also known as the Josephson junction) displaying negative differential resistance, was employed to construct a device capable of amplifying weak microwave signal reflections from it. This device can be operated near the intrinsic precision limits set by the Heisenberg's uncertainty principle. Arrays of Superconducting Quantum Interference Devices (SQUIDs), operated below the critical current, can be used for metamaterial resonators whose resonant frequency can be quickly modulated by magnetic flux. These devices are operated as parametric amplifiers and they are capable of amplifying weak microwave signals near the quantum limit of noise. But more importantly, they are capable of perturbing the vacuum itself, which creates correlated photon pairs seeded by vacuum fluctuations. This effect is known as the dynamical Casimir effect (DCE) and is demonstrated in this thesis work by using power and correlation measurements at microwave frequencies. Furthermore, investigations on the DCE have been extended using a double modulation scheme yielding vacuum-induced coherence and tripartite correlations. Nanocarbon devices have also been studied in this thesis, in particular a wideband low noise nanotube electrometer constructed from a nanotube with proximity induced superconductivity. This device has certain unique benefits when operated in a microwave environment which are discussed in the thesis. Another nanocarbon device, a double quantum dot constructed from graphene and superconducting leads has been used to demonstrate Cooper-pair splitting. This device operates as a tunable source of entangled electrons.
Properties of weak links between two superconductors, or Josephson junctions, make them interesting for fundamental physics research. Since their discovery over four decades ago, they have provided a unique way to study the behavior of the superconducting quantum phase. More recently, ultra small, or mesoscopic, Josephson junctions with substantial single Cooper pair charging energy have gained interest due to their behavior as macroscopic quantum objects. In addition to the theoretical interest, Josephson junctions can be used as active elements in circuit applications. Particularly, in this Thesis we study two different devices. We develop the required theoretical treatments, derive device properties, and compare the results with experimental data. The first application is a Josephson voltage standard based on externally damped Superconductor - Insulator - Superconductor junctions. It consists of an array of large Josephson junctions connected in series and irradiated with a 70 GHz microwave signal. Phase locking the Josephson dynamics into the signal leads to the quantization of the voltage. This is utilized in metrology. We introduce a new circuit solution based on frequency dependent damping of the junctions. Optimization and some designs for practical arrays are presented. The purpose is to find such a design that the array is fast, has low power consumption and is as stable as possible. Arrays able to generate DC voltages of order 1 volt with metrological accuracy are demonstrated experimentally and their applicability in AC voltage calibrations is analyzed. The second application is the Bloch Oscillating Transistor (BOT). The BOT is based on controlling the Cooper pair current in an ultra small Josephson junction by means of quasiparticles tunneling through a normal junction. As part of the thesis work, the principle of operation is first demonstrated computationally. The model is then refined to yield quantitative predictions of the characteristics. Finally, an analytic theory for the device is developed and the properties as an amplifier are derived.
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.
The work involves a study of physical phenomena that take place at very small length scales, below one micro-meter. At temperatures roughly below one degree Kelvin, quantum-mechanical effects may rule in electronic transport. Macroscopic quantum-coherent effects that occur in metallic superconducting microstructures, are particularly intriguing. Large-scale quantum information processing is widely believed to be attainable utilizing such physical systems. This work concentrates on answering the question of how the described quantum-mechanical systems may be used as sensitive measuring devices. Considerable attention is paid to energy-storing metallic microstructures whose electrical properties resemble those of the familiar inductor or capacitor. This research involves primarily experimental investigations conducted around temperatures of 0.1 Kelvin. Methods both at low and at radio frequencies have been used. The experimental findings have been modelled theoretically, and theoretical concepts for new physical phenomena have been introduced. An inductively measured radio-frequency Cooper-pair transistor, the L-SET, has been developed and experimentally verified in this work. Being highly sensitive, fast, and non-invasive, the L-SET appears to be the most promising method for measuring electric charge. Sensitivity in charge measurements of 20 millionths of the electron charge (micro-e) within one second, and an input bandwidth of 100 MHz, have been demonstrated. It has been shown theoretically that the ultimate measurement accuracy is about 0.1 micro-e within a second. A new phase detector based on the Cooper-pair transistor has been proposed. This system has also been shown to be potentially usable as a quantum bit. A new type of radio-frequency single-electron transistor built using a multi-walled carbon nanotube has been fabricated and operated. Technologies have been developed in order to make the physical nano- or microstructures. A method has been presented to fabricate non-superconducting tunnel junctions. Consequences of the inverse superconducting proximity effect on the studied superconducting structures were considered. Measurement procedures were investigated for a new low-noise nanoamplifier, the Bloch-oscillating transistor. Single superconducting tunnel junctions were tested as detectors of energy states of the environment, or of noise.
We propose a new type of cryogenic current amplifiers, in which low-frequency power spectrum of current can be measured through a measurement of microwave response of a superconducting resonant circuit shunted by a series array of Josephson junctions. From numerical analysis on the equivalent circuit, the numerical value of the input-referred current noise of the proposed amplifier is found to be two orders of magnitude lower than the noise floor measured with the conventional cryogenic current amplifiers based on high-electron-mobility transistors or superconducting quantum interference devices. Our proposal can open new avenues for investigating low-temperature solid-state devices that require lower noise and wider bandwidth power spectrum measurements of current.