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Physical Review A

Thermal noise effects on the microwave-induced steps of a current-driven Josephson junction

Eshel Ben‐Jacob, David J. Bergman

Published Apr 1, 1984• 31 citations
Publisher

Abstract

We study the effects of thermal noise on the microwave-induced steps of a current-driven Josephson junction using the resistively shunted junction model for the junction. We generalize Stephen's method for calculating the width of the steps to the case of an underdamped junction, and to the case of a subharmonic step, provided that there is no overlapping of different steps. In order to treat the case of overlapping steps we introduce a new approach which enables us to calculate the distribution of fluctuations about as well as the transition rates out of the steps. All our results are usually in the form of explicit analytical expressions that facilitate a comparison with experiments.

DOI
10.1103/physreva.29.2021

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International Journal of Nano and Biomaterials•Jan 1, 2009•0 citations
We study the effects of thermal noise on the microwave-induced steps of a current-driven Josephson junction using the resistively shunted junction model for the junction. We generalize Stephen's method for calculating the width of the steps to the case of an underdamped junction, and to the case of a subharmonic step, provided that there is no overlapping of different steps. In order to treat the case of overlapping steps we introduce a new approach which enables us to calculate the distribution of fluctuations about as well as the transition rates out of the steps. All our results are usually in the form of explicit analytical expressions that facilitate a comparison with experiments.
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.
We consider a current biased, resistively shunted josephson junction irradiated at two frequencies. The perturbation technique introduced by Aslamasov and Larkin is used in the calculations. Both signals are treated as perturbations. The second order calculation yields the size of the mixing steps atV_{\pm}=h(\omega_{1}\pm\omega_{2})/2e. As in the case of a single frequency we show that subharmonic mixing steps are absent. The amplitude of the voltage oscillation at the difference and sum frequencies is shown to be non-zero at all voltages. We calculate the microwave resistance for one frequency ω2to third order in the perturbation. There are negative resistance regions nearV\pm(as well as nearV_{2}= h\omega_{2}/2e). Near V, the negative resistance region appears for bias voltage V just aboveV_{-}, while near V the region appears for V just belowV_{+}. This means that when an incident frequency mixes with a cavity mode the mixing step atV_{-}will be inverted compared to the cavity step itself.
High Tc Josephson junctions have IcRn products as large as a few mV at liquid helium temperature, and hence, the frequency normalized by IcRn∕Φ0 becomes on the order of 10−3 for a gigahertz (GHz) microwave signal. (Here, Ic, Rn, and Φ0 are the critical current, the normal resistance, and a flux quantum, respectively.) It is well known that a microwave-current-driven Josephson junction does not exhibit clear Shapiro steps under such low frequency conditions. Instead of Shapiro steps, however, we often observe a current-step-like structure in the current–voltage curve of YBa2Cu3O7−δ grain boundary Josephson junctions coupled to a GHz signal. In this article, we present a model analysis for such current-step-like structures. Two types of device models are employed: a simple resistively and capacitively shunted junction model and a rf-field-driven two-junction superconducting quantum interference device model. Numerical results of the latter model agree with the experimental results, which indicates that the envelope of small Shapiro steps, including the effects of microwave-induced motion of flux quanta, appears as a current-step-like structure in a high Tc Josephson device coupled to a GHz microwave.
An experimental investigation is made of the subharmonic Shapiro steps observed on the I-V curves of high-T c superconductor Josephson junctions and on the bias-voltage dependences of the rf noise and detector response when the junctions are subjected to external submillimeter radiation. Structures of this type are ordinarily described by a nonsinusoidal current-phase relation, which is why subharmonic steps appear. Numerical modeling of the processes occurring in a Josephson junction by means of a simple current-phase relation, as in the case of an SNS junction, gives good agreement with experiment. The width of the characteristic Josephson generation line of the junction was estimated on the basis of the noise dependences and the selective detector response. The width can be explained by taking into account the shot noise of the tunneling component of the conductivity. A model of the conductivity of a high-T c superconductor Josephson junction, consisting of a tunnel junction with microshorts possessing metallic conductivity, is discussed.
I-V characteristics of Josephson junction (JJ) under microwave irradiation is simulated taking the resistance, capacitance and inductance of the junction (RCLSJ) into account. Since most of the JJ made with high TC material operates at high temperature where the thermal fluctuation is playing significant role. In the present simulation, thermal noise is also taken into consideration and simulated result explains the rounding behaviour of the Shapiro step observed in the experimental I-V curve. The simulated results also confirm the growing of Shapiro steps with increasing microwave power. This model also clearly account for the appearance of broad minima and reduction of the maxima in the power dependence of the step amplitude ΔIn/2Ic as observed in the experimental data of Kautz et al. (1992).