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Physical review. B, Condensed matter

Nonlinear microwave absorption in weak-link Josephson junctions

Lei Xie, Jarek Wosik, John C. Wolfe

Published Dec 1, 1996• 21 citations

Abstract

A model, based on the resistively shunted junction theory, is developed and used to study microwave absorption in weak-link Josephson junctions in high-${T}_{c}$ superconductors. Both linear and nonlinear cases of microwave absorption in Josephson junctions are analyzed. A comparison of the model with microwave absorption loop theory is presented along with a general condition for the applicability of both models. The nonlinear case was solved numerically and the threshold points of sharp microwave absorption are presented. At these points, a $2\ensuremath{\pi}$ phase quantization takes place within each microwave cycle, leading to an onset of a sharp rise of absorption. Existence of the $2\ensuremath{\pi}$ dynamic quantization is the key to the interpretation of nonlinear microwave absorption data. The nonlinear microwave absorption model is extended to the study of nonuniformly coupled junctions, and a general statement for the applicability of such a model is presented.

DOI: 10.1103/physrevb.54.15494

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arXiv:1802.06438•Physical review. B./Physical review. B•Jun 27, 2018•9 citations

A model, based on the resistively shunted junction theory, is developed and used to study microwave absorption in weak-link Josephson junctions in high-

{T}_{c}

superconductors. Both linear and nonlinear cases of microwave absorption in Josephson junctions are analyzed. A comparison of the model with microwave absorption loop theory is presented along with a general condition for the applicability of both models. The nonlinear case was solved numerically and the threshold points of sharp microwave absorption are presented. At these points, a

2\ensuremath{\pi}

phase quantization takes place within each microwave cycle, leading to an onset of a sharp rise of absorption. Existence of the

2\ensuremath{\pi}

dynamic quantization is the key to the interpretation of nonlinear microwave absorption data. The nonlinear microwave absorption model is extended to the study of nonuniformly coupled junctions, and a general statement for the applicability of such a model is presented.

The electrophysics and microwave properties of Niobium oxide-barrier tunnel junctions with critical current densities up to 105A/cm2were studied. Millimeter wave mixing using strong nonlinearity of quasi-particle tunnelling curve is described. Nonhysteretic Josephson junctions obtained by the low inductance resistive shunting of the tunnel structures were investigated in the large frequency band. The frequency range where these junctions obey the resistively shunted junction model was determined. The shunted tunnel junctions have been shown to be suitable for various applications which require stable enough Josephson junctions with nonhysteretic I-V curve (IVC).

Double-barrier Josephson junctions, with outer electrodes of superconducting Nb and a central thin layer of non-superconducting Al, are being developed as self-shunted junctions for high-frequency superconducting integrated circuits. This paper presents a simplified phenomenological model of the behaviour of such junctions (often called SINIS, for superconductor-insulator-normal-insulator-superconductor) based on the resistively shunted junction model, using Josephson coupling between the layers and the time-dependent Ginzburg-Landau equation to describe the dynamics of the weak induced energy gap in the Al layer. This analysis shows how non-hysteretic I - V characteristics can be obtained but suggests some limitations in their high-frequency performance. Predictions for critical current generally agree with prior experiments. The technological implications of this model are discussed.

Experimental I-V curves of microwave-driven Josephson tunnel junctions with resistive shunts are reported. The results are in very good agreement with numerical calculations using the resistively shunted junction model. In the low-frequency regime there are three distinct regions in the I-V curves and two different types of Shapiro steps. It is demonstrated that the overall shape of the I-V curves can be explained by using an adiabatic interpretation of the junction response. The two different types of Shapiro steps are related to a compensation effect between dc and rf bias currents.

A Josephson tunnel junction which is rf driven near a dynamical bifurcation point can amplify quantum signals. However, the bifurcation point will exist robustly only if the electrodynamic environment of the junction meets certain criteria. We develop a general formalism for dealing with the nonlinear dynamics of a Josephson junction embedded in an arbitrary microwave circuit. We find sufficient conditions for the existence of the bifurcation regime: (a) the embedding impedance of the junction needs to present a resonance at a particular frequency ${\ensuremath{\omega}}_{R}$, with the quality factor

Q

of the resonance and the participation ratio

p

of the junction satisfying

Qp⪢1

, and (b) the drive frequency should be low frequency detuned away from ${\ensuremath{\omega}}_{R}$ by more than $\sqrt{3}{\ensuremath{\omega}}_{R}∕(2Q)$.

The microwave absorption and noise caused by quantum two-level systems (TLSs) dramatically suppress the coherence in Josephson junction qubits that are promising candidates for quantum information applications. It is a challenge to understand microwave absorption by TLSs because of the spectral diffusion resulting from fluctuations in their resonant frequencies induced by their long-range interactions. Here we treat the spectral diffusion explicitly using the generalized master equation formalism. The proposed theory predicts that the linear absorption regime holds while a TLS Rabi frequency is smaller than their phase decoherence rate. At higher external fields, a nonlinear absorption regime is found with the loss tangent inversely proportional to the intensity of the field. The theory can be generalized to acoustic absorption and lower dimensions realized in superconducting qubits.