Dc SQUID: Noise and optimization

Abstract

A computer model is described for the dc SQUID in which the two Josephson junctions are nonhysteretic, resistively shunted tunnel junctions. In the absence of noise, current-voltage(I–V) characteristics are obtained as functions of the applied flux, Φ a , SQUID inductanceL, junction critical currentI 0 , and shunt resistanceR. The effects of asymmetry inL, I 0 , andR are discussed.I–V characteristics, flux-voltage transfer functions, and low-frequency spectral densities of the voltage noise are obtained at experimentally interesting values of the parameters in the presence of Johnson noise in the resistive shunts. The transfer functions and voltage spectral densities are used to calculate the flux and energy resolution of the SQUID operated as an open-loop, small-signal amplifier. The resolution of the SQUID with ac flux modulation is discussed. The flux resolution calculated for the SQUID of Clarke, Goubau, and Ketchen is1.6 × 10 −5 Φ 0 Hz−1/2 , approximately one-half the experimental value. Optimization of the SQUID resolution is discussed: It is shown that the optimum operating condition is β=2LI 0 /Φ 0 ≈1. Finally, some speculations are made on the ultimate performance of the tunnel junction dc SQUID. When the dominant noise source is Johnson noise in the resistive shunts, the energy resolution per Hz is4k B T(πLC) 1/2 , whereC is the junction capacitance, and the constraintR=(Φ 0 /2πCI 0 ) 1/2 has been imposed. This result implies that the energy resolution is proportional to (junction area) 1/2 . In the limiteI 0 R ≫k B T, the dominant noise source is shot noise in the junctions; for β=1, the energy resolution per Hz is then approximatelyh/2.