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Soviet Journal of Low Temperature Physics

Effect of energy relaxation in a superconductor on the response of an rf squid

I. M. Dmitrenko, V. A. Khlus, Georgy M. Tsoi, V. I. Shnyrkov

Published Jul 1, 1983• 0 citations
Publisher

Abstract

We consider how energy relaxation in a superconductor affects the macroscopic quantum interference effects that occur in a ring closed by a Josephson junction. It is demonstrated experimentally that the behavior of such a ring when the external parameters are altered differs radically from the properties suggested by the resistive model. The effects revealed may well be explained by the microscopic theory which takes account of the energy relaxation time of excitations in the superconductor.

DOI
10.1063/10.0030920

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Physical review. B, Condensed matter•Feb 1, 1990•2 citations
We consider how energy relaxation in a superconductor affects the macroscopic quantum interference effects that occur in a ring closed by a Josephson junction. It is demonstrated experimentally that the behavior of such a ring when the external parameters are altered differs radically from the properties suggested by the resistive model. The effects revealed may well be explained by the microscopic theory which takes account of the energy relaxation time of excitations in the superconductor.
The behavior of a superconducting ring incorporating a point contact, coupled inductively to an oscillatory circuit (hf SQUID), with the rate of change of the magnetic flux in the ring being comparable, to the inverse energy relaxation time of excitations in the superconductor τϵ−1, is examined. For T ∽ Tc the results of the microscopic theory of the nonstationary behavior of point contacts, in which the coupling between the phase difference and the current of the Josephson junction differs from the usual expression I = V/R + Icsinφ in the resistive model, are used. It is shown that the nonequilibrium behavior of a weak link for ω≳τϵ−1 significantly changes the amplitude–frequency and signal characteristics of the SQUID as compared with the case ωτϵ−1≪1, for which the results based on the resistive model are valid. The characteristics of the SQUID in the nonequilibrium situation are sensitive to the ratio between the size of the contact and the mean free path of electrons relative to scattering by impurities.
The dynamics of a small Josephson junction, driven either by a current source or by an external flux when the junction is the weak link element of a SQUID ring, were studied. Approximate analytical arguments and numerical simulations were used for the lumped circuit model of the junction. The various characteristic times of these devices were systematically obtained as functions of the parameters G and K of the junction and of the SQUID, respectively. The forms of the flux transitions and the times governing them are obtained for linear and periodic time variations of the external flux on the SQUID. A coupling of the SQUID to an LC circuit was treated. Limitations on the device parameters consistent with fast response, stability, and sensitivity were obtained both for the current driven junction and for the rf SQUID.
The impedance and noise of a resistive superconductive quantum interference device (R-SQUID) have been measured as a function of the dc and rf currents applied to it. The Josephson junction was adjustable so that data were also taken for several values of the junction critical current. The results were compared with the predictions of a resistively shunted junction (RSJ) model which takes into account the influence of the Josephson junction on the impedance and noise. The agreement was found to be quite good and demonstrates that the noise in the circuit is well understood. Use of the R-SQUID as a noise thermometer below 1 K is assessed in terms of corrections due to the RSJ model. It is demonstrated how the dc and rf currents may be adjusted so that the total noise of the R-SQUID is reduced to within 0.1% of the Johnson noise generated by the resistor alone. Under these conditions, the R-SQUID may be used as a noise thermometer to determine thermodynamic temperature to this inaccuracy from 6 to 700 mK.
In this paper we explore the quantum behavior of a superconducting quantum-interference device (SQUID) ring which has a significant Josephson coupling energy. We show that the eigenfunctions of the Hamiltonian for the ring can be used to create macroscopic quantum superposition states of the ring. We also show that the ring potential may be utilized to squeeze coherent states. With the SQUID ring as a strong contender as a device for manipulating quantum information, such properties may be of great utility in the future. However, as with all candidate systems for quantum technologies, decoherence is a fundamental problem. In this paper we apply an open systems approach to model the effect of coupling a quantum-mechanical SQUID ring to a thermal bath. We use this model to demonstrate the manner in which decoherence affects the quantum states of the ring.
Based on the hypothesis that the macroscopic superconducting shielding current on the surface of a porous granular superconductor is short lived due to the action of thermal noise, a dispersive-mode theory for a high-temperature radio-frequency superconducting quantum interference device (rf SQUID) is suggested. In this theory, the effect of the SQUID ring on the resonant tank circuit is an effective inductance Le{L}_{e}Le​, Le{L}_{e}Le​=k2{k}^{2}k2FLT{\mathrm{FL}}_{T}FLT​, where k is the coupling coefficient between the SQUID ring and the resonant tank circuit with inductance LT{L}_{T}LT​, and F is a periodic function of external flux ${\ensuremath{\Phi}}_{\mathrm{dc}}$ with a period of flux quantum ${\ensuremath{\Phi}}_{0}$. The phenomena that the weak-link-rf-SQUID flux-receiving area defined by the hole of the SQUID ring and the bulk-rf-SQUID flux-receiving area, which is determined by an annular surface region with a thickness of the effective penetration depth ${\ensuremath{\lambda}}_{e}$, can be interpreted. The theory is qualitatively consistent with available experimental results.