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Soviet Journal of Low Temperature Physics

Effect of nonequilibrium phenomena in a superconducting point contact on the properties of a single-contact quantum interferometer

V. A. Khlus

Published Jan 1, 1984• 0 citations
Publisher

Abstract

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.

DOI
10.1063/10.0031040

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Journal of Applied Physics•Sep 1, 1973•56 citations
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 electrical equations of a resonant circuit fed with a radio-frequency current and inductively coupled to a weakly superconducting loop have been derived. The current-voltage characteristic of the rf superconducting quantum interference device can then be calculated and studied as a function of the junction resistance or of the resonance frequency, enabling its behavior to be better understood. As shown by Kurkijärvi, the large positive slope of the steps and the rounding of the characteristic result from thermal noise. However, in order to explain quantitatively the experimental results concerning, namely, point contact weak links which are generally oxidized or which have several contact points, it is useful to remark that the connection between the two superconductors constituting the Josephson junction may be made from n resistive paths. The mean thermal energy of the fluctuating flux is then close to nkbT instead of kbT if the inductances linking the contact points are large enough, that is, on the order of 10−11 H.
This paper reports the results of an experimental and phenomenological investigation of the static and dynamic behavior of weakly connected superconducting rings. The configuration is essentially a macroscopic superconducting ring of inductance LLL incorporating a point contact as a weak link which determines the critical supercurrent in the ring, ic{i}_{c}ic​. A phenomenological model for the stationary quantum states of the system as a function of an applied field is developed. The dynamic behavior is obtained directly from the time dependence of the applied fields. Experiments demonstrating both the stationary and the time-dependent magnetic behavior are described. The stationary behavior was obtained with a magnetometer incorporating a weakly connected ring as a sensor to measure the flux through the ring under test. The experimental results confirm the phenomenological model if the critical curr\`ent ic{i}_{c}ic​ is greater than $\frac{{\ensuremath{\Phi}}_{0}}{2L(1+\ensuremath{\gamma})}$, where ${\ensuremath{\Phi}}_{0}=\frac{h}{2e}$ is the flux quantum and $\ensuremath{\gamma}$ is a material and geometric parameter which is usually small compared to unity. In the regime $L{i}_{c}>\frac{{\ensuremath{\Phi}}_{0}}{2(1+\ensuremath{\gamma})}$, the quantum states are discrete, and the transitions between states are well defined and irreversible. If the critical current is not too large, the transitions generally occur only between adjacent states; that is, $\ensuremath{\Delta}k=\ifmmode\pm\else\textpm\fi{}1$. At large critical current, multiple quantum jumps are observed. On the other hand, if $L{i}_{c}<\frac{{\ensuremath{\Phi}}_{0}}{2(1+\ensuremath{\gamma})}$, the quantum states merge into one another continuously and reversibly. In this case the magnetic behavior inthe neighborhood of the half-quantum points is related to the depairing or gapless regime in superconductivity. Measurements of the ac properties of the weakly connected ring at 30 MHz are interpreted directly in terms of the static properties under the influence of a time-varying applied field. In fact, no qualitative corrections to the theory are expected up to frequencies of the order of the superconducting energy gap.
The mechanisms of the decay of metastable current states in the superconducting loop of an rf SQUID in the hysteresis state are studied. Clamped point contacts are used as the Josephson weak link. The first derivative of the radio-frequency IVC dVT/dIRF, which gives the dependence of the decay probability density on the amplitude of the oscillations of the magnetic flux in the ring, was measured experimentally. Studies of the temperature dependence of the width of the probability distribution in the interval from 4.2 to 0.5 K show that for most high-resistance Nb–Nb, Nb–Ag–Nb contacts the quantum mechanisms of decay become dominant at a temperature of the order of 2 K. The experimentally measured parameters of the decay probability distribution in the quantum limit are compared with the theoretical values calculated based on the theory of macroscopic quantum tunneling in the limit of strong and weak dissipation. The experimental magnitude of the width of the probability density as well as the characteristic quantum temperature exceed the theoretical values, which can be explained by the deviation of the current-phase dependence of the contact from a sinusoidal dependence. In addition, some contacts apparently correspond to the case of an intermediate magnitude of dissipation. When the frequency of the rf oscillations changed from 30 to 6 MHz, the width of the distribution remained unchanged, which follows from the theory of quantum tunneling decay of the metastable current state in the loop in the limit of strong damping. At low temperatures (T ∼ 50 K) and for a sufficiently small damping coefficient, anomalous peaks were observed in the probability density with an amplitude of the rf oscillations significantly smaller than the critical magnitude of the magnetic flux in the loop.
In this thesis we present theoretical investigations of the effects of Andreev bound states on the current transport in superconducting interferometers. We also investigate the slow dynamics of the Andreev states in a superconducting point contact, and the possible application as a quantum bit. We consider superconductor-normal metal-superconductor (SNS) and normal metalsuperconductor (NS) interferometers, where the contact region is a Y-shaped normal metal wave guide, and the two connection points to the same superconducting electrode can have different phases. The electric current in the interferometer is calculated as a function of the applied voltage and the phase difference . Andreev reflection in SNS and NS interferometers incorporates two features: interference in the arms of the Y-shaped normal region, and interplay with Andreev resonances. The latter feature yields rich phase dependent current structures in the subgap voltage region. The interference effect leads to a suppression of the current structures at . We investigate the effects on the Josephson current in NS interferometers due to current injection from the normal electrode. The two main effects of the nonequilibrium situation are: nonequilibrium population of the Andreev levels, which can result in enhancement, suppression, or even sign reversal of the Josephson current, and an anomalous interference Josephson effect, which gives rise to a long range Josephson effect, increasing with the voltage up to the superconducting gap . The two Andreev states in a superconducting quantum point contact can be accessed for manipulation and measurement by embedding the point contact in a superconducting loop. We calculate an effective Hamiltonian for the slow dynamics of the Andreev two-level system in the ring. Furthermore, we discuss methods of manipulation of the Andreev levels, and coupling of qubits. The state of the Andreev two-level system can be read out by monitoring the macroscopic quantum tunneling in a current biased Josephson junction, which is embedded in the superconducting ring of the qubit. We discuss the effects on the qubit, the readout scheme and the signal-to-noise ratio. THESIS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY Coherent processes in Superconducting quantum interferometers and qubits
A simple theory of the superconducting single-junction interferometer (ac Squid) becomes possible if the critical current of the single junction is small relative to Φ0/LR, where Φ0=h/2e is one flux quantum and LR is the inductance of the interferometer loop. This theory predicts a magnetic flux sensitivity which has the same dependence on interferometer parameters as the existing theories for higher critical currents. In contrast to those theories, however, the present theory predicts that the maximum flux sensitivity will be achieved off resonance. Theoretical predictions for comparison with experiment are displayed as a function of the normalized difference between the operating frequency ω and the resonant frequency ω0.