A Numerical Treatment of the Rf SQUID: II. Noise Temperature
Abstract
We investigate rf SQUIDs (Superconducting QUantum Interference Devices), coupled to a resonant input circuit, a readout tank circuit and a preamplifier, by numerically solving the corresponding Langevin equations and optimizing model parameters with respect to noise temperature. We also give approximate analytic solutions for the noise temperature, which we reduce to parameters of the SQUID and the tank circuit in the absence of the input circuit. The analytic solutions agree with numerical simulations of the full circuit to within 10%, and are similar to expressions used to calculate the noise temperature of dc SQUIDs. The best device performance is obtained when {beta}{sub L}{prime} {triple_bond} 2{pi}LI{sub 0}/{Phi}{sub 0} is 0.60.8; L is the SQUID inductance, I{sub 0} the junction critical current and F{sub 0} the flux quantum. For a tuned input circuit we find an optimal noise temperature T{sub N,opt} {approx} 3Tf/f{sub c}, where T, f and f{sub c} denote temperature, signal frequency and junction characteristic frequency, respectively. This value is only a factor of 2 larger than the optimal noise temperatures obtained by approximate analytic theories carried out previously in the limit {beta}{sub L}{prime} << 1. We study the dependence of the noise temperature on various model parameters, and givemore »
 Authors:
 Publication Date:
 Research Org.:
 COLLABORATION  U.Tubingen/Germany
 OSTI Identifier:
 928721
 Report Number(s):
 LBNL62298(II)
Journal ID: ISSN 00222291; JLTPAC; R&D Project: 504801; BnR: KC0202020; TRN: US0803251
 DOE Contract Number:
 DEAC0205CH11231
 Resource Type:
 Journal Article
 Resource Relation:
 Journal Name: Journal of Low Temperature Physics; Journal Volume: 149; Journal Issue: 56; Related Information: Journal Publication Date: 12/2007
 Country of Publication:
 United States
 Language:
 English
 Subject:
 75; CRITICAL CURRENT; INDUCTANCE; LANGEVIN EQUATION; PERFORMANCE; TANK CIRCUITS
Citation Formats
Kleiner, Reinhold, Koelle, Dieter, and Clarke, John. A Numerical Treatment of the Rf SQUID: II. Noise Temperature. United States: N. p., 2007.
Web. doi:10.1007/s1090900795129.
Kleiner, Reinhold, Koelle, Dieter, & Clarke, John. A Numerical Treatment of the Rf SQUID: II. Noise Temperature. United States. doi:10.1007/s1090900795129.
Kleiner, Reinhold, Koelle, Dieter, and Clarke, John. Mon .
"A Numerical Treatment of the Rf SQUID: II. Noise Temperature". United States.
doi:10.1007/s1090900795129. https://www.osti.gov/servlets/purl/928721.
@article{osti_928721,
title = {A Numerical Treatment of the Rf SQUID: II. Noise Temperature},
author = {Kleiner, Reinhold and Koelle, Dieter and Clarke, John},
abstractNote = {We investigate rf SQUIDs (Superconducting QUantum Interference Devices), coupled to a resonant input circuit, a readout tank circuit and a preamplifier, by numerically solving the corresponding Langevin equations and optimizing model parameters with respect to noise temperature. We also give approximate analytic solutions for the noise temperature, which we reduce to parameters of the SQUID and the tank circuit in the absence of the input circuit. The analytic solutions agree with numerical simulations of the full circuit to within 10%, and are similar to expressions used to calculate the noise temperature of dc SQUIDs. The best device performance is obtained when {beta}{sub L}{prime} {triple_bond} 2{pi}LI{sub 0}/{Phi}{sub 0} is 0.60.8; L is the SQUID inductance, I{sub 0} the junction critical current and F{sub 0} the flux quantum. For a tuned input circuit we find an optimal noise temperature T{sub N,opt} {approx} 3Tf/f{sub c}, where T, f and f{sub c} denote temperature, signal frequency and junction characteristic frequency, respectively. This value is only a factor of 2 larger than the optimal noise temperatures obtained by approximate analytic theories carried out previously in the limit {beta}{sub L}{prime} << 1. We study the dependence of the noise temperature on various model parameters, and give examples using realistic device parameters of the extent to which the intrinsic noise temperature can be realized experimentally.},
doi = {10.1007/s1090900795129},
journal = {Journal of Low Temperature Physics},
number = 56,
volume = 149,
place = {United States},
year = {Mon Jan 15 00:00:00 EST 2007},
month = {Mon Jan 15 00:00:00 EST 2007}
}

We investigate the characteristics and noise performance of rf Superconducting Quantum Interference Devices (SQUIDs) by solving the corresponding Langevin equations numerically and optimizing the model parameters with respect to noise energy. After introducing the basic concepts of the numerical simulations, we give a detailed discussion of the performance of the SQUID as a function of all relevant parameters. The best performance is obtained in the crossover region between the dispersive and dissipative regimes, characterized by an inductance parameter {beta}{prime}{sub L} {triple_bond} 2{pi}LI{sub 0}/{Phi}{sub 0} {approx} 1; L is the loop inductance, I{sub 0} the critical current of the Josephson junction,more »

Theory of the signal transfer and noise properties of the rf SQUID
The forward and reverse interactions between the SQUID input and output via the weak link are investigated in detail and presented in the form of an electronic equivalent circuit of the SQUID. The input and output impedances and the gain of the SQUID are given. The noise properties for all kinds of source impedances are computed and optimal values derived. 
Input noise in the hysteretic rf SQUID: Theory and experiment
The spectral density of the lowfrequency opencircuit intrinsic input noise of the hysteretic rfbiased SQUID is calculated. The noise level, which affects the optimized power sensitivity of the SQUID, is found to be strongly model dependent and thus also constitutes an interesting probe of device physics. The results of the calculation are significantly different from previous predictions. A direct measurement of the total input noise of a typical rfbiased SQUID system is reported. The results, which are consistent our calculation, correspond to a system noise temperature of 3.1 + 0.4 mK at a frequency of 1 kHz. This value ismore » 
Influence of the tank circuit noise on the dc impedance of the rfbiased RSQUID
The tank circuit noise in an rfbiased RSQUID noise thermometer is shown to have a small but a detectable influence on the dc impedance of the resistively shunted Josephson junction. The result supplements earlier calculations which have been used to explain some of the experimentally observed characteristics of the dc impedance.