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arXiv:cond-mat/9805174 · Low Temperature Physics

Magnetic flux locking in two weakly coupled superconducting rings

R. de Bruyn Ouboter, A. N. Omel’yanchuk, E. D. Vol

Published Oct 1, 1998• 3 citations
arXivHTMLPDF

Abstract

We have analyzed the quantum interference effects in the macroscopic “superconducting molecule.” The composite system consists of two massive superconducting rings, each interrupted by a Josephson junction, which are at the same time weakly coupled with one another. The special case of coupling via the Josephson four-terminal junction is considered. The structure of the macroscopic quantum states in an applied magnetic field is calculated. It is shown that, depending on the values of the magnetic fluxes through each ring, the system displays two groups of states, the “orthostates” with both induced currents going in the same direction, and the “parastates” with the opposite currents and with the total induced flux locked to zero value. The transition to the flux locked state with changing of the total applied flux is sudden and is preserved in a certain interval which is determined by the difference of the fluxes applied through each ring. It makes the system sensitive to small gradients of the external magnetic field.

DOI
10.1063/1.593669

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We have analyzed the quantum interference effects in the macroscopic “superconducting molecule.” The composite system consists of two massive superconducting rings, each interrupted by a Josephson junction, which are at the same time weakly coupled with one another. The special case of coupling via the Josephson four-terminal junction is considered. The structure of the macroscopic quantum states in an applied magnetic field is calculated. It is shown that, depending on the values of the magnetic fluxes through each ring, the system displays two groups of states, the “orthostates” with both induced currents going in the same direction, and the “parastates” with the opposite currents and with the total induced flux locked to zero value. The transition to the flux locked state with changing of the total applied flux is sudden and is preserved in a certain interval which is determined by the difference of the fluxes applied through each ring. It makes the system sensitive to small gradients of the external magnetic field.
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.
A study is made of the effects of quantum interference in weakly coupled superconducting systems in an external magnetic field, allowance being made for fluctuations. The circulating supercurrent is found as a function of the applied magnetic field for a weakly coupled ring when the coupling is comparable in magnitude with the thermal energy. The current--voltage characteristic for a superconducting quantum interferometer is found and it is shown that the amplitude of the steps formed in the current--voltage characteristic under the influence of external irradiation is an oscillating function of the flux of the applied magnetic field with a period equal to the flux quantum. (AIP)
This paper investigates the physical nature of a series of step structures or oscillations present in a Josephson current within one magnetic flux quantum when either a Josephson junction, a double junction squId, or a single junction superconducting ring is placed inside a high Q cavity under the condition in which the Josephson frequency is equal to the resonance frequency of the cavity. The frequency effect of the feedback field produces a series of induced current steps in the Josephson junction or the two-junction squId when ..omega.. = ..omega../sub r/. The oscillating electromagnetic field excited by the junction current acts on the junction itself. A series of new current step structures occur within one magnetic flux phi/sub 0/ quantum, since the amplitude of the feedback field is modulated by an applied magnetic field as the modulation of the amplitude of the feedback field is coupled to that of the radiation. For the superconducting ring containing a single junction, as n..omega.. = ..omega../sub r/, the feedback radiation of the stationary electromagnetic wave will give rise to a constrained oscillation of the supercurrent with a period smaller than that of the superconducting current oscillation phi/sub 0/.
Abstract Superconducting quantum interference devices (SQUIDs) are made by a superconducting loop interrupted by one or more Josephson junctions. They are described in terms of a macroscopic variable, the magnetic flux, which shows quantum effects such as tunnelling through a potential barrier. Besides making up the source of a quantum state, SQUIDs also provide the instruments necessary for its probing: as a fact, SQUID based magnetometers have a sensitivity approaching the quantum limit. In this paper I will review the working principle of these devices and illustrate the system of SQUIDs realized in my group to test the quantum behavior at a macroscopic level.
We investigate the behavior of dual three-Josephson-junction loops coupled through a mutual inductance in the classical regime. The energy levels and the circulating currents in the loops are calculated as a function of applied external magnetic flux. The calculation shows that the coupling effect leads to the sequential reversal of the circulating currents in the loops. We measured the magnetic flux due to the circulating currents with a DC-SQUID in a flux-locked loop configuration. We demonstrate that the states of the coupled system can be manipulated with a magnetic field. The observed magnetic flux agrees very well with the simulation results based on the measurement of an inductance associated with a superconducting wire. The observed reversal of the circulating currents is explained in terms of the noise-activated escape from the metastable state in a six-dimensional potential.
The Hamiltonian of a superconducting thin loop interrupted by a double-barrier Josephson junction is derived. The parameter ε, which takes account of the difference in the Josephson coupling of the two single junctions in the SISIS structure, is seen to allow variation of the energy gap ΔE01 between the ground state and the first excited flux number state of the system. An additional parameter γ, describing the coupling between the outer electrodes of the double-barrier Josephson junction, is introduced. Persistent currents in the system are studied in terms of the usual parameter α, representing the ratio between the Josephson energy and the magnetic energy, and of the externally applied flux.