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

TL;DR

This paper numerically and analytically investigates the noise temperature of rf SQUIDs coupled to resonant circuits, optimizing parameters for minimal noise and comparing results with theoretical predictions.

Contribution

It provides a combined numerical and analytical analysis of rf SQUID noise temperature, including parameter optimization and realistic device considerations.

Findings

Optimal noise temperature occurs at specific  values (0.6-0.8).

Analytic solutions agree within 10% with numerical simulations.

The minimal noise temperature is approximately 3Tf/f_c, close to previous theoretical limits.

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_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.