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Acta Physica Sinica

THE SUPERCURRENT OSCILLATIONS WITHIN ONE FLUX QUANTUM PERIOD φ0 FOR WEAK LINKS (Ⅱ)——THE SUPERCONDUCTING RING CONTAINING A WEAK LINK

CHENG GENG-HUA, ZHANG YU-HENG, (1)中国科学技术大学物理系,合肥; (2)中国科学技术大学物理系,研究生

Published Jan 1, 1982• 0 citations
Publisher

Abstract

It is pointed out that if a superconducting ring containing a weak link is placed in a cavity, which is in resonant with the current flowing in the ring, i.e., when the frequency of the Josephson current or one of its n-th harmonies is equal to the cavity frequency, and if the cavity has sufficiently high Q-value, then the feedback of the stationary electric-magnetic wave will act on the ring itself and produce a small sinusoidal oscillation superposing on the primary sawtooth wave oscillating current. The period of the small oscillation will be φ0/n and its amplitude that of the sawtooth wave multiplied by 1/nπ.

DOI
10.7498/aps.31.932

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Journal of Physics Condensed Matter•Sep 29, 1997•7 citations
It is pointed out that if a superconducting ring containing a weak link is placed in a cavity, which is in resonant with the current flowing in the ring, i.e., when the frequency of the Josephson current or one of its n-th harmonies is equal to the cavity frequency, and if the cavity has sufficiently high Q-value, then the feedback of the stationary electric-magnetic wave will act on the ring itself and produce a small sinusoidal oscillation superposing on the primary sawtooth wave oscillating current. The period of the small oscillation will be φ0/n and its amplitude that of the sawtooth wave multiplied by 1/nπ.
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/.
In this paper, we analyzed the physical essence for producing a series of step structures or oscillating effect of dc Josephson current within one flux quantum period φ0 by placing Josephson junction, two-junction SQUID and the supercon ducting ring containing a single junction in a cavity, when one of the eigen-frequencies ωr of which is equal to Josephson frequency and the Q-Value is sufficiently high. We point out that the frequency effect of the feedback field would produce a series of induced steps for Josephson junction or two-junction SQUID, as ω = ωr, the oscillating electric-magnetic field excited by the junction current reacts on the junctions themself. Furthermore, a series of new step structures should occur within the φ0 since the amplitude of the feedback field is modulated by applied magnetic field as the modulation of the amplitude of the feedback field is coupled with that of the radiation. For the superconducting ring containing a single junction, as nω=ωr, the feedback radiation of stationary electric-magnetic wave will give rise constrained oscillation of the supereurrent with a smaller period than the φ0.
If a SQUID consisting of two junctions is placed in a cavity with sufficiently high Q-value, when the Josephson frequency of the junction ω=2eV0/h equals to one of the ei-gen frequencies ωr of the cavity, then the oscillating electromagnetic field in the form of standing wave excited by the junction current would react on the junctions and produce a series of steps of dc Josephson current within one flux quantum period Φ0. The theory also predicts that a series of new superconducting quantum interference phe-nomenons would be produced by Josephson currents of two junctions in the feed back field. The step height of the Josephson current will be inreased when both junctions are placed separately at the peak of the standing wave. The phase of the interference trace of SQUID will change by π/2 when one of the junctions is placed at the peak and the other is placed at the trough. The I-H trace of SQUID will degenerate to that of signle junction when one of the junctions is placed at the pack and the other is placed at the node. The step will not occur except that with n=0 yhen both junctions are placed separately at nodes.
Voltage biasing of a single superconducting weak link results in coherent electromagnetic oscillation at the frequency $\ensuremath{\nu}=\frac{V}{{\ensuremath{\Phi}}_{0}}$; simultaneous voltage biasing of two weak links in a superconducting ring produces two strongly coupled oscillators at the same frequency. The electromagnetic phase difference is the difference in the gauge-invariant quantum phases across the two contacts. Because of the quantization of the superconducting ring, this phase difference is $\frac{2\ensuremath{\pi}〈\ensuremath{\Phi}〉}{{\ensuremath{\Phi}}_{0}}$, where $〈\ensuremath{\Phi}〉$ is the time-averaged magnetic flux in the superconducting circuit and ${\ensuremath{\Phi}}_{0}$ is the flux quantum. We can characterize the coupled system in terms of normal modes, and we have experimentally observed these modes of oscillation at 30 MHz. This provides a means of understanding the earlier observations of quantum interference in the resistive state.
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.
Starting with a simple Lagrangian for the electromagnetic field with broken gauge symmetry, we derive an effective circuit Hamiltonian for a superconducting weak-link ring. The energy eigenstates of this Hamiltonian exhibit sensitivity to both external magnetic flux and an applied Faraday law voltage. We show that the flux periodicity of the rf SQUID ring, and the voltage periodic behaviour found in ultra-small-capacitance weak-link rings, can be seen as limiting cases of a more general phenomenon.