A Numerical Treatment of the Rf SQUID: II. Noise Temperature

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_L'\equiv 2\pi L I_0\Phi_0 is 0.6 - 0.8; L is the SQUID inductance, I_0 the junction critical current and \Phi_0 the flux quantum. For a tuned input circuit we find an optimal noise temperature T_{N,opt}\approx 3Tf/f_c, where T, f and f_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_L'<<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.Comment: submitted to J. Low Temp. Phy

Statistical Theory of Spin Relaxation and Diffusion in Solids

A comprehensive theoretical description is given for the spin relaxation and diffusion in solids. The formulation is made in a general statistical-mechanical way. The method of the nonequilibrium statistical operator (NSO) developed by D. N. Zubarev is employed to analyze a relaxation dynamics of a spin subsystem. Perturbation of this subsystem in solids may produce a nonequilibrium state which is then relaxed to an equilibrium state due to the interaction between the particles or with a thermal bath (lattice). The generalized kinetic equations were derived previously for a system weakly coupled to a thermal bath to elucidate the nature of transport and relaxation processes. In this paper, these results are used to describe the relaxation and diffusion of nuclear spins in solids. The aim is to formulate a successive and coherent microscopic description of the nuclear magnetic relaxation and diffusion in solids. The nuclear spin-lattice relaxation is considered and the Gorter relation is derived. As an example, a theory of spin diffusion of the nuclear magnetic moment in dilute alloys (like Cu-Mn) is developed. It is shown that due to the dipolar interaction between host nuclear spins and impurity spins, a nonuniform distribution in the host nuclear spin system will occur and consequently the macroscopic relaxation time will be strongly determined by the spin diffusion. The explicit expressions for the relaxation time in certain physically relevant cases are given.Comment: 41 pages, 119 Refs. Corrected typos, added reference

MEASUREMENTS OF SQUID EQUIVALENT CIRCUIT PARAMETERS

Un circuit equivalent complet pour le SQUID-rf a été présenté par Ehnholm. Nous présentons des mesures qui vérifient ce circuit et démontrent ses propriétés.A complete equivalent circuit for the rf SQUID has been presentated earlier by Ehnholm. Measurements that verify and demonstrate its properties are presented

CRYOGENIC GaAs-FET AMPLIFIERS FOR SQUIDS

Nous avons mis au point des préamplificateurs cryogéniques pour SQUIDs. .Ils utilisent des transistors à effet de champ à l'arseniure de gallium. La sensibilité de l'ensemble est limitée par le bruit intrinsèque du SQUID et est 5 x 10-30 J/Hz à 500 MHz. Nous discutons les critères de conception à l'aide d'un circuit équivalent pour faibles signaux.Gallium arsenide field effect transistor amplifiers for use with SQUIDs at 4.2 K in the frequency range 50 - 500 MHz have been developed. The system sensibility is limited by intrinsic SQUID noise and is 5 x 10-30 J/Hz à 500 MHz. Design criteria and practical limitations are discussed in terms of small signal equivalent circuits

NUCLEAR SPIN-LATTICE RELAXATION TIME IN TIN

Les temps de relaxation nucléaire spin-réseau de 119Sn et 117Sn on été mesurés entre 20 et 50 mK à l'aide d'un magnétomètre à SQUID en suivant la restauration de l'aimantation longitudinale après une impulsion R. F. La température a été déterminée à l'aide d'un thermomètre à bruit couplé à un SQUID. Les constantes de Korringa ont été estimées d'après les valeurs de τ1. Nous discutons les possibilités d'application de cette méthode a la thermomètrie.The nuclear spin-lattice relaxation times for 119Sn and 117Sn have been measured in the temperature range between 20 and 50 mK with a SQUID magnetometer by watching the recovery of the longitudinal magnetization of the nulear spins after the application of an rf-pulse. The temperature was determined using a SQUID noise thermometer. The Korringa constants were estimated from the τ1-values. Application of the method for thermometry is discussed