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Applied Physics Letters

Transfer function and thermal noise of YBa2Cu3O7−δ direct current superconducting quantum interference devices operated under large thermal fluctuations

K. Barthel, D. Koelle, Boris Chesca, Alex I. Braginski, Achim Marx, R. Gross, R. Kleiner

Published Apr 12, 1999• 10 citations
Publisher

Abstract

Direct current superconducting quantum interference devices (SQUIDs) made from high transition temperature superconductors typically exhibit a still unexplained higher white noise and smaller transfer function than numerical simulations based on the coupled Langevin equations predict. We present a systematic study that compares experimental results with both numerical simulations and a recently developed analytical approach based on a Fokker–Planck equation. To cover a wide range of SQUID parameters, two samples of different inductances were measured at variable temperature. While several predictions of the analytical theory could be verified and a good qualitative agreement with both theories is observed, only one sample showed good quantitative agreement. Furthermore, our simulations performed in the limit of large thermal fluctuations show excellent agreement with the analytic theory.

DOI
10.1063/1.123803

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Direct current superconducting quantum interference devices (SQUIDs) made from high transition temperature superconductors typically exhibit a still unexplained higher white noise and smaller transfer function than numerical simulations based on the coupled Langevin equations predict. We present a systematic study that compares experimental results with both numerical simulations and a recently developed analytical approach based on a Fokker–Planck equation. To cover a wide range of SQUID parameters, two samples of different inductances were measured at variable temperature. While several predictions of the analytical theory could be verified and a good qualitative agreement with both theories is observed, only one sample showed good quantitative agreement. Furthermore, our simulations performed in the limit of large thermal fluctuations show excellent agreement with the analytic theory.
A symmetric superconducting quantum interference device (SQUID) with two Josephson junctions in the presence of thermal fluctuations is theoretically studied through two-dimensional Fokker-Planck equations. An analytical formula of the SQUID transfer function (or responsitivity) is derived by using the potential condition in the case of the steady state. It is found that the relationship between the optimum bias current I opt and the thermal fluctuation parameter Γ is I opt /Γ>1. The optimal reduced dc SQUID inductance β opt is in the range of 0.80<β opt <1.25, which is remarkably in agreement with the result of numerical simulation β opt ≈1.
Properties of white noise of a high-Tc dc superconducting quantum interference device (SQUID) have been studied using numerical simulation. It is shown that thermal noise at T=77 K significantly affects the noise properties of the SQUID. As a result, dependencies of noise properties on inductance become quite different from conventional results at T=4.2 K. In contrast to the case T=4.2 K, the voltage noise of the SQUID at T=77 K depends very weakly on the inductance, while the transfer function degrades rapidly with inductance. Consequently, rapid degradation of flux noise with inductance, as compared with the case T=4.2 K, is caused mainly by that of the transfer function. These simulation results explain reasonably experimental results reported recently. Therefore, it is necessary to improve the transfer function for the improvement of noise properties in the case of large inductances. Numerical simulation shows that a method for improving the transfer function using resistively shunted inductance or three Josephson junctions, which was proposed by the authors, is also useful for improving noise properties in the case of large inductances.
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.
Effects of thermal noise on the characteristics of the dc superconducting quantum interference device (SQUID) have been studied. Numerical simulation on the SQUID characteristics operating at T=77 K has been performed by taking into account the thermal noise. It is shown that the voltage versus flux relation of the dc SQUID is degraded considerably with the thermal noise. The degradation becomes significant when the inductance of the SQUID increases. Due to this degradation, there exists significant limitation for the range of the inductance available at T=77 K, unlike the case at T=4.2 K. The maximum inductance should be around 200 pH in order to avoid significant degradation of the transfer function. This limited value of the inductance must be taken into account when we realize the SQUID coupled to an input coil. The analytical expression for the degradation of the transfer function due to the thermal noise is also obtained. The theoretical result explains experimental results reported recently.
An analytical expression for the stationary probability distribution of the DC superconducting quantum interference device (SQUID) with a resistively shunted inductance driven by thermal noise is derived from the two-dimensional Fokker–Planck equation. The effects on the SQUID characteristics subject to a large thermal fluctuation with a noise parameter Γ>0.20 are discussed by taking into account the thermal noise in the accuracy of numerical simulation. This theory is valid for a reduced inductance β⩽1. The analytical formulae for the SQUID characteristics, e.g. the circulating current, the average voltage and the voltage modulation, are obtained and discussed. The theory shows that the voltage modulation increases with the shunted inductance more efficiently for a large inductance parameter β and small fluctuation parameter Γ.
We have studied white (high-frequency)-noise properties of YBa2Cu3O7-δ grain-boundary dc superconducting quantum interference devices (SQUIDs). Bias voltage (V) dependence of the white-noise voltage spectral density (S v) was measured for dc-SQUIDs and junctions. As a result, S v at low bias voltage can be explained by the thermal noise theory of tunnel junctions. Furthermore, the energy resolution of 1.96×10-32 J/Hz is obtained at 43 K in the white-noise region. The measured energy resolution of the dc-SQUIDs is in good agreement with the theoretical results. According to the above results, YBa2Cu3O7-δ dc-SQUIDs with a quantum noise limit might be realized at 4.2 K.