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Journal of Applied Physics

Quantum Phase Noise in Superconductors: Temperature Dependence Measured by Quantum Interference Techniques with Point-Contact Josephson Junctions

B. T. Ulrich

Published Apr 1, 1969• 0 citations
Publisher

Abstract

Thermodynamic fluctuations limit the ultimate performance of superconducting devices of practical interest, devices such as the quantum interference magnetometer and the Josephson junction radiation detector. We report direct observations of thermodynamically driven quantum phase fluctuations near the superconducting critical temperature. The experiments used point-contact quantum interference techniques with niobium points on a single-crystal tin substrate. Near the superconducting transition of tin, TC=3.72°K, the niobium points served as probes to measure fluctuations in the phase of the superconducting order parameter within the tin crystal. The temperature was slowly increased, beginning well below TC for tin, where the quantum phase was stable. Quantum phase fluctuations were first observed approximately 5 mdeg below TC. As the temperature continued to increase through this 5 mdeg range near TC, the characteristic frequency of the phase fluctuations increased 6 orders of magnitude. At TC a discontinuous transition to a resistive state gave rise to a finite voltage difference in the tin with the associated driven quantum phase precession. Thermodynamic Johnson noise voltages developed across this resistance of order 10−10Ω observably broadened the precession line. We will present the detailed temperature dependence of the frequency power spectrum of quantum phase fluctuations below and above TC.

DOI
10.1063/1.1657935

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Thermodynamic fluctuations limit the ultimate performance of superconducting devices of practical interest, devices such as the quantum interference magnetometer and the Josephson junction radiation detector. We report direct observations of thermodynamically driven quantum phase fluctuations near the superconducting critical temperature. The experiments used point-contact quantum interference techniques with niobium points on a single-crystal tin substrate. Near the superconducting transition of tin, TC=3.72°K, the niobium points served as probes to measure fluctuations in the phase of the superconducting order parameter within the tin crystal. The temperature was slowly increased, beginning well below TC for tin, where the quantum phase was stable. Quantum phase fluctuations were first observed approximately 5 mdeg below TC. As the temperature continued to increase through this 5 mdeg range near TC, the characteristic frequency of the phase fluctuations increased 6 orders of magnitude. At TC a discontinuous transition to a resistive state gave rise to a finite voltage difference in the tin with the associated driven quantum phase precession. Thermodynamic Johnson noise voltages developed across this resistance of order 10−10Ω observably broadened the precession line. We will present the detailed temperature dependence of the frequency power spectrum of quantum phase fluctuations below and above TC.
We have measured the low-frequency noise in the critical current Ic of six dc superconducting quantum interference devices (SQUIDs) with resistively shunted Nb–NbOx–PbIn Josephson junctions in the temperature range T=0.09–4.2K. Each device is voltage biased, the applied flux is an integer number of flux quanta, and the current fluctuations are measured with a second dc SQUID. At low frequencies f, there is a component of the power spectrum of the critical current fluctuations given approximately by SIc(f)=CIc2T2∕Af, where A is the area of both junctions, and C≈(3.9±0.4)×10−23m2∕K2. For quantum bits based on Josephson junctions, the scaling of SIc(f) with T2 implies that the dephasing time limited by critical current l∕f noise should scale as 1∕T for temperatures down to at least 0.09K.
At low temperatures non-equilibrium voltage fluctuations can be generated in current-biased superconducting nanowires due to proliferation of quantum phase slips (QPS) or, equivalently, due to quantum tunneling of magnetic flux quanta across the wire. In this paper we review and further extend recent theoretical results related to this phenomenon. Employing the phase-charge duality arguments combined with Keldysh path integral technique we analyze such fluctuations within the two-point and four-point measurement schemes demonstrating that voltage noise detected in such nanowires in general depends on the particular measurement setup. In the low frequency limit we evaluate all cumulants of the voltage operator which turn out to obey Poisson statistics and exhibit a power law dependence on the external bias. We also specifically address a non-trivial frequency dependence of quantum shot noise power spectrum SΩ for both longer and shorter superconducting nanowires. In particular, we demonstrate that SΩ decreases with increasing frequency Ω and vanishes beyond a threshold value of Ω at T → 0. Furthermore, we predict that SΩ may depend non-monotonously on temperature due to quantum coherent nature of QPS noise. The results of our theoretical analysis can be directly tested in future experiments with superconducting nanowires.
de Broglie wave interferometers have been constructed, successfully utilizing extended superconducting links of tin to couple coherently the quantum phases of two Josephson junctions. The current transmitted by these devices was periodic in the enclosed flux (periodicity (.9 ± .3) h/2e) demonstrating unambiguously coherence of the superconducting order parameter over 1.33 meters. We may define a Josephson junction as one for which the quantum mechanical coupling energy is insufficient to overcome the disruptive effects of noise. Consequently, the relative phase of the coupled superconductors is not stabilized and the zero Josephson current fluctuates, (bandwidth ~ 2eVnoise/h) averaging to zero. Two such junctions have been coupled to an electromagnetic cavity formed by the superconducting arms of a quantum interferometer (junction separation 1. 33 meters). With an applied steady voltage such that the Josephson current excites a normal mode of the cavity, a coherent radiation field is built up. This coherent radiation feeds back to the junctions forcing time coherence on the phase precession, resulting in a dynamic stabilization of the junctions. Under these conditions a series of constant voltage has been observed in the I-V characteristic of one interferometer. The Josephson frequency associated with these steps is shown to be characteristic of the electromagnetic resonant modes of the cavity. Frequency modulation analysis, combined with a detailed analysis of the cavity-junction combination, predicts such maxima in the tunneling of pairs when a selection rule, (m + n) even, is obeyed. Here m/2 is the number of flux quanta (h/2e) linking the interferometer and n is the order of the cavity resonance excited. Experimental confirmation of the detailed predictions of the analysis is presented.
Following a method proposed by Divin and Modovets [Sov. Tech. Phys. Lett. 9, 108 (1983)], we have measured at millimeter waveband the intrinsic noise temperatures TN of YBa2Cu3O7−δ Josephson junctions or dc superconducting quantum interference devices (SQUIDs) fabricated on SrTiO3, yttria-stabilized ZrO2, or Si bicrystal substrates. Over wide ranges of physical temperatures TP and the junction’s normal resistance RN, it was found that TN follows TP pretty well. This indicates that the intrinsic noise in the devices is dominated by Johnson noise. TN was also measured in cases where there is external magnetic field applied, or where there is another microwave radiation like the local oscillator in a mixer. The magnetic field or microwave radiation does not seem to affect TN in any appreciable way. To estimate the high frequency performance of the junctions on Si bicrystal substrates, direct irradiation by a far infrared laser at 1.81 THz is carried out and the clear first Shapiro step is observed.
We measured the amplitude–frequency characteristics of radio frequency superconducting quantum interference devices (rf SQUIDs) over a temperature range between 65 and 79 K. Using the expressions derived from the recently developed rf SQUID theory, valid also at large thermal fluctuations, we determined from these data the basic parameters of high-transition-temperature superconductor (HTS) rf SQUIDs. These parameters were: (a) the high-frequency coupling coefficient between the rf SQUID and the tank circuit resonator, k, (b) the SQUIDs hysteretic parameter, β, (c) the critical current of the Josephson junction, Ic, (d) its normal resistance, Rn, and (e) its noise parameter, Γ. We found a good agreement with the values of β(Ic) and Rn determined directly after destructively opening the SQUID loop. In accordance with the theoretical predictions, our experimental results show that at large thermal fluctuation levels (T≅77 K), rf SQUIDs with large loop inductance operate in nonhysteretic mode up to β values exceeding 3. Furthermore, we have shown that the optimal energy sensitivity is attained in the nonhysteretic mode at a value of β distinctly higher than 1. A quantitative comparison of white noise predicted by the theory with that obtained from the experiment showed a reasonable agreement. We also discussed the contribution of the phase information to the SQUID’s signal and noise at optimum operation conditions, when a mixer was used as a signal detector.
The impedance and noise of a resistive superconductive quantum interference device (R-SQUID) have been measured as a function of the dc and rf currents applied to it. The Josephson junction was adjustable so that data were also taken for several values of the junction critical current. The results were compared with the predictions of a resistively shunted junction (RSJ) model which takes into account the influence of the Josephson junction on the impedance and noise. The agreement was found to be quite good and demonstrates that the noise in the circuit is well understood. Use of the R-SQUID as a noise thermometer below 1 K is assessed in terms of corrections due to the RSJ model. It is demonstrated how the dc and rf currents may be adjusted so that the total noise of the R-SQUID is reduced to within 0.1% of the Johnson noise generated by the resistor alone. Under these conditions, the R-SQUID may be used as a noise thermometer to determine thermodynamic temperature to this inaccuracy from 6 to 700 mK.