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arXiv:1312.3298 · New Journal of Physics

Direct spectrum analysis using a threshold detector with application to a superconducting circuit

Grégoire Ithier, Giovanna Tancredi, P. J. Meeson

Published May 14, 2014• 5 citations
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Abstract

We introduce a new and quantitative theoretical framework for noise spectral analysis using a threshold detector, which is then applied to a superconducting device: the Josephson bifurcation amplifier. We show that this new framework provides direct access to the environmental noise spectrum with a sensitivity approaching the standard quantum limit of weak continuous measurements. In addition, the accessible frequency range of the spectrum is, in principle, limited only by the ring down time of the resonant mode. This on-chip noise detector is non-dissipative and works with low probing powers, allowing it to be operated at low temperatures ( mK). We exploit this technique for measuring the frequency fluctuations of our device and find a low frequency noise with an amplitude and spectrum compatible with a dielectric origin.

DOI
10.1088/1367-2630/16/5/055010

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We introduce a new and quantitative theoretical framework for noise spectral analysis using a threshold detector, which is then applied to a superconducting device: the Josephson bifurcation amplifier. We show that this new framework provides direct access to the environmental noise spectrum with a sensitivity approaching the standard quantum limit of weak continuous measurements. In addition, the accessible frequency range of the spectrum is, in principle, limited only by the ring down time of the resonant mode. This on-chip noise detector is non-dissipative and works with low probing powers, allowing it to be operated at low temperatures ( mK). We exploit this technique for measuring the frequency fluctuations of our device and find a low frequency noise with an amplitude and spectrum compatible with a dielectric origin.
The Josephson Bifurcation Amplifier is a threshold detector that may be viewed as a 1-bit analog-to-digital converter. Such a device is subject to two random processes, firstly the bifurcation itself is a dynamical process that is subject to quantum or thermal fluctuations that broaden the threshold, secondly the device is immersed in an environment that induces low frequency parametric noise. We have developed a new measurement technique that quantitatively and directly links the environmental noise spectrum to the spectrum calculated from the repetitively acquired binary output of the Josephson Bifurcation Amplifier. The technique has considerable advantages over the NMR techniques presently in common use for studies of qubit decoherence and the techniques used for SQUIDs. It is non-dissipative, enabling operation in the milliKelvin range, it has a wide bandwidth, it is operated at low photon numbers, and its sensitivity approaches the shot noise limit of a weak continuous measurement.
Using a quantum detector, a superconductor-insulator-superconductor junction, we probe separately the emission and absorption noise in the quantum regime of a superconducting resonant circuit at equilibrium. At low temperature the resonant circuit exhibits only absorption noise related to zero point fluctuations, whereas at higher temperature emission noise is also present. By coupling a Josephson junction, biased above the superconducting gap, to the same resonant circuit, we directly measure the noise power of quasiparticles tunneling through the junction at two resonance frequencies. It exhibits a strong frequency dependence, consistent with theoretical predictions.
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.
By coupling a quantum detector, a superconductor-insulator-superconductor junction, to a Josephson junction via a resonant circuit we probe the high-frequency properties, namely the ac complex admittance and the current fluctuations of the Josephson junction at the resonant frequencies. The admittance components show frequency-dependent singularities related to the superconducting density of states while the noise exhibits a strong frequency dependence, consistent with theoretical predictions. The circuit also allows us to probe separately the emission and absorption noise in the quantum regime of the superconducting resonant circuit at equilibrium. At low temperature the resonant circuit exhibits only absorption noise related to zero-point fluctuations, whereas at higher temperature emission noise is also present.
Electrical engineers and physicists are naturally very interested in noise in circuits, amplifiers and detectors. With the advent of quantum computation and other high frequency electronics operating at low temperatures, we have entered a regime where quantum noise and quantum-limited detectors are important. Here we describe the general concept of a two-level system as a quantum spectrum analyzer and apply it to a simple superconducting qubit, the Cooper-pair box. We then discuss the coupling of a Cooper-pair box to its electromagnetic environment, whose noise leads to a finite polarization and excited-state lifetime of the qubit. Finally, we describe a theoretical technique for treating a qubit coupled to a measurement system, which allows one to calculate the full quantum noise of the measurement device. We present results for such a calculation for the case of a normal SET.
Quantum mechanics can strongly influence the noise properties of mesoscopic devices. To probe this effect we have measured the current fluctuations at high-frequency (5-90G Hz) using a superconductor-insulator-superconductor tunnel junction as an on-chip spectrum analyzer. By coupling this frequency-resolved noise detector to a quantum device we can measure the high-frequency, non-symmetrized noise as demonstrated for a Josephson junction. The same scheme has been used to detect the current fluctuations arising from coherent charge oscillations in a two-level system, a superconducting charge qubit. A narrow band peak was observed in the spectral noise density at the frequency of the coherent charge oscillations.