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arXiv:1507.04884 · Physical Review Applied

Shot Noise of a Quantum Dot Measured with Gigahertz Impedance Matching

T. Hasler, M. Jung, V. Ranjan, Gabriel Puebla‐Hellmann, Andreas J. Wallraff, Christian Schönenberger

Published Nov 3, 2015• 19 citations
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Abstract

Modern experiments using high-speed, high-impedance devices such as quantum dots can suffer from strong suppression of signal power, if components are not carefully impedance-matched. To overcome this problem, the authors show that a resonant impedance-matching circuit based on superconducting transmission lines can improve the signal to noise ratio by nearly three orders of magnitude. This technology is particularly important to noise studies of electron transport in quantum systems, which can provide information that is unattainable by other means.

DOI
10.1103/physrevapplied.4.054002

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Modern experiments using high-speed, high-impedance devices such as quantum dots can suffer from strong suppression of signal power, if components are not carefully impedance-matched. To overcome this problem, the authors show that a resonant impedance-matching circuit based on superconducting transmission lines can improve the signal to noise ratio by nearly three orders of magnitude. This technology is particularly important to noise studies of electron transport in quantum systems, which can provide information that is unattainable by other means.
It can be hard to find that perfect match---even, or perhaps especially, in quantum electronics. Microwave readout of highly Ohmic quantum devices, like superconducting qubits, necessitates impedance-matching circuits to maximize power transfer. $L\phantom{\rule{0}{0ex}}C$ resonant circuits enjoy two major advantages over well-established coplanar transmission-line circuits: larger bandwidths (and thus shorter readout times), and drastically smaller on-chip footprints. With this in mind, the authors develop a compact $L\phantom{\rule{0}{0ex}}C$ resonator operating at 3 GHz to bridge a load of ~15 k$\mathrm{\ensuremath{\Omega}}$ to a typical coaxial line at 50 $\mathrm{\ensuremath{\Omega}}$---match made.
Coupling carbon nanotube devices to microwave circuits offers a significant increase in bandwidth (BW) and signal-to-noise ratio. These facilitate fast non-invasive readouts important for quantum information processing, shot noise and correlation measurements. However, creation of a device that unites a low-disorder nanotube with a low-loss microwave resonator has so far remained a challenge, due to fabrication incompatibility of one with the other. Employing a mechanical transfer method, we successfully couple a nanotube to a gigahertz superconducting matching circuit and thereby retain pristine transport characteristics such as the control over formation of, and coupling strengths between, the quantum dots. Resonance response to changes in conductance and susceptance further enables quantitative parameter extraction. The achieved near matching is a step forward promising high-BW noise correlation measurements on high impedance devices such as quantum dot circuits. Radio-frequency circuits offer fast low-noise detection of signals in carbon nanotubes, but incompatibilities in fabrication degrade the performance of the hybrid device. Here, the authors use a deterministic mechanical transfer to couple pristine nanotubes to a gigahertz superconducting matching circuit.
Fast measurement of small currents and even smaller fluctuations in devices with large impedance is not trivial. Standard low frequency lock-in measurements suffer from stray capacitance of the order of nF reducing the bandwidth to merely kHz and a time resolution of ms. One approach of increasing the bandwidth is to connect the high-impedance device next to a low input impedance amplifier, though, the signal is decreased by the ratio of the impedances of the device and the amplifier, easily a factor of a thousand. Therefore, long averaging times are required to detect the small signal. Moreover, 1/f noise still affects the measurements. The issues of small bandwidth, impedance mismatch and 1/f noise can be simultaneously addressed using resonant LC circuits. The success of this impedance transformer lies in replacing the slow operation of applying voltages and measuring currents by applying fast radio frequency signals and measuring the reflectance. LC circuits remain appealing because of a rather simple assembly. Nonetheless, the challenge to reproducibly achieve the resonance frequencies in gigahertz (GHz) range while matching to high impedance still remains due to the large parallel stray capacitance of the measurement setup. Resonance frequency in GHz range is desirable for two reasons. Firstly, measurements are faster and 1/f noise smaller. Yet more importantly, one can profit from the wide range of measurement techniques developed in the context of circuit quantum electrodynamics, such as FPGA based hardware and quantum limited Josephson parametric amplifiers. \n \nIn this thesis, a matching circuit namely stub tuner based on coplanar transmission lines is designed, fabricated and integrated with mesoscopic devices. Owing to the simple design, we could predict the frequency response of a stub tuner in terms of the standard circuit model (Chapter 3). We initiated certain necessary fabrication adaptations to achieve integration of niobium circuits with devices. In particular, a reliable stamping of carbon nanotubes from the growth substrate to the target substrate was accomplished, improving both the device quality and yield (Chapter 4). RF reflectometry is employed to perform admittance measurements on CNT quantum dots. We could reliably deduce all circuit and device properties using the resonance response. The measurement bandwidth is shown to be in MHz range which is three orders of magnitude larger than that for DC measurements. In particular, using the phase response of the circuit, double-dot qubit energy and dephasing rate are studied (Chapter 5). We could even get rid of conventional contacts that could degrade the device properties, and still extract quantum capacitance and dissipation in graphene p-n junctions. The residual doping is shown to affect not only the mean free path but also the Fermi velocity. We further see that at small doping, electron-electron interactions could modify the Fermi velocity and that the dispersion relation could deviate from linearity (Chapter 6). \n \nIn the second half of the scientific results, real strength of stub tuner is tested in transmission measurements. The large bandwidth and signal to noise ratio is utilized to measure extremely clean noise power densities at high speed and draw comparisons with the corresponding average current. Clear changes in the shot noise spectrum are seen when a transport channel is added or removed from the bias window of the quantum dot. We especially observe noise enhancement outside the Coulomb diamonds due to blocking states (Chapter 7). Finally, we investigate noise properties of quantum dots when leads are superconducting. Distinct charge transfers due to multiple Andreev reflections are visible in the shot noise. The main finding, however, was the thermal noise at zero bias. We observed its periodic suppression and emergence across the quantum dot resonance. In another device, shot noise due to the Kondo effect is found to be enhanced in the superconducting state when the Kondo temperature exceeds the value of the superconducting gap (Chapter 8). Simple design and reliable calibration of the GHz matching circuit in both reflectance and transmission pave a way for fast and non-invasive measurements of mesoscopic conductors. \n \n \n \n \n
Coherent circuits based on superconducting elements hold tremendous promise for the practical implementation of quantum information technology: advanced computation, cryptography, and hardware simulation of complex materials systems are envisioned applications. Such circuits are essentially engineered atoms with level transitions in the 4-8 GHz regime; as such “read” and “write” operations are performed with the aid of fast microwave pulses and low-noise amplifiers, respectively. Recent advances in cavity-based superconducting parametric amplifiers have enabled real-time measurement and feedback in one and two qubits. We demonstrate a novel Josephson junction transmission-line based traveling-wave amplifier which employs sub-wavelength phase matching resonators to achieve high gain, several GHz of bandwidth, and near quantum-noise limited performance. Such devices will enable multiplexed qubit readout in integrated architectures comprised of a variety of microwave frequency analog and digital superconducting technologies: signal sources, multiplexers, ADCs, DACs, mixers, and amplifiers.
We report the efficient coupling of a 50 Ω microwave circuit to a high impedance conductor. We use an impedance transformer consisting of a λ/4 co-planar resonator whose inner conductor contains an array of superconducting quantum interference devices (SQUIDs), providing it with a tunable lineic inductance L∼80 μ0, resulting in a characteristic impedance ZC∼1 kΩ. The impedance matching efficiency is characterized by measuring the shot noise power emitted by a dc biased tunnel junction connected to the resonator. We demonstrate matching to impedances in the 15 to 35 kΩ range with bandwidths above 100 MHz around a resonant frequency tunable between 4 and 6 GHz.