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arXiv:cond-mat/0504122 · Applied Physics Letters

Charge sensitivity of the inductive single-electron transistor

Mika A. Sillanpää, Leif Roschier, Pertti Juhani Hakonen

Published Aug 19, 2005• 9 citations
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Abstract

We calculate the charge sensitivity of a recently demonstrated device where the Josephson inductance of a single Cooper-pair transistor is measured. We find that the intrinsic limit to detector performance is set by oscillator quantum noise. Sensitivity better than 10−6e∕Hz is possible with a high Q value ∼103, or using a superconducting quantum interference device amplifier. The model is compared to experiment, where charge sensitivity 3×10−5e∕Hz and bandwidth 100 MHz are achieved.

DOI
10.1063/1.2034096

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We calculate the charge sensitivity of a recently demonstrated device where the Josephson inductance of a single Cooper-pair transistor is measured. We find that the intrinsic limit to detector performance is set by oscillator quantum noise. Sensitivity better than 10−6e∕Hz is possible with a high Q value ∼103, or using a superconducting quantum interference device amplifier. The model is compared to experiment, where charge sensitivity 3×10−5e∕Hz and bandwidth 100 MHz are achieved.
Here, we report the operation of a superconducting single-electron transistor (S-SET) as a fast and nearly quantum-limited charge-sensitive amplifier. By operating the S-SET such that Cooper pair tunneling is resonant across both of its tunnel junctions, we are able to achieve an excellent charge sensitivity of δq = 1.6 × 10-6e/√(Hz), while also minimizing back action. We find that near its optimal operating point, the S-SET can have both a very low noise temperature Tn≈ 50 mK and a large power gain ASET>;>; 1. These results indicate that our S-SET operates within a factor of 2 of the quantum limit.
We demonstrate a sensitive method of charge detection based on radio-frequency readout of the Josephson inductance of a superconducting single-electron transistor. Charge sensitivity 1.4 x 10(-4) e/square root Hz, limited by a preamplifier, is achieved in an operation mode which takes advantage of the nonlinearity of the Josephson potential. Owing to reactive readout, our setup has more than 2 orders of magnitude lower dissipation than the existing method of radio-frequency electrometry. With an optimized sample, we expect uncoupled energy sensitivity below variant Planck's over h in the same experimental scheme.
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.
Using an operator scattering approach, we analyze the quantum dynamics of an ultrasensitive electrometer—a Cooper pair transistor embedded in a quarter-wave microwave cavity (cCPT). While the cCPT is inherently a tunable, strongly nonlinear system affording a diverse range of functionalities, we restrict our present analysis to a necessary first investigation of its linear charge sensing capabilities, limiting to low pump powers corresponding to an average cavity photon number of ≲1. Assuming realizable cCPT parameters [B. L. Brock et al., Phys. Rev. Applied 15, 044009 (2021)], and not including noise from the subsequent amplifier chain, we predict the fundamental, photon shot noise-limited charge sensitivity to be 0.12μe/Hz when the pumped cavity has an average of one photon and the cCPT is operated close to charge degeneracy. This is to be compared with a first reported charge sensitivity value of 14μe/Hz in the single-photon regime [B. L. Brock et al., arXiv:2102.05362 (2021)].
A Single-Electron Transistor (SET) is a highly sensitive charge amplifier based on the Coulomb blockade that can operate near the quantum limit: amplification can be accomplished with a back-action close to that required by the uncertainty principle. Its charge sensitivity is ultimately limited to about 1micre/sqrt(Hz) by the shot noise in the source-drain current. Despite the fact that such sensitivity has been approached by some, the shot-noise limit has yet to be reached for either the SET and its RF version, the RF-SET. A scheme is proposed and realized in this thesis for the shot noise-limited detection of a Single-Electron Transistor, based on a DC-SQUID impedance-matched with a DC-biased SET. SQUIDs can operate at the quantum limit, and a microstrip SQUID amplifier has already been demonstrated to operate at almost twice the quantum-limited noise temperature at about 500MHz by M. Muck and collaborators, with a sensitivity sufficient to resolve the SET shot noise. The device has been fabricated and characterized. A 50KOhm resistor has been used as a noise source at low temperature and the measured noise levels have been estimated. Moreover, the detection noise temperature of about 110mK was derived corresponding to a current sensitivity of about 8fA/sqrt(Hz) for the detection of a 100KOhm resistor.
Using a classical equation of motion, dynamics of the phase is analyzed in the Inductive Single-Electron Transistor (L-SET) which is a promising new system suitable for quantum measurement with ultimate sensitivity and low back-action. In a regime of nonlinear dynamics, a shift of the oscillator resonant frequency is discovered which has a direct analogy to the switching of a dc-biased Josephson junction into voltage state. Results are reviewed for the predicted charge sensitivity, and it is shown that a performance challenging the best rf-SETs is foreseeable with the new device.