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Physical Review

Noise in a Driven Josephson Oscillator

Michael J. Stephen

Published Oct 10, 1969• 66 citations
Publisher

Abstract

The effect of noise on the microwave-induced steps in the current-voltage characteristic of a Josephson junction is investigated theoretically. The dynamic resistance of a step is obtained in the limit that the capacitance of the junction is small. The phase fluctuations of the junction are greatly reduced in the presence of the microwave signal, and the dynamic resistance can be extremely small.

DOI
10.1103/physrev.186.393

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The effect of noise on the microwave-induced steps in the current-voltage characteristic of a Josephson junction is investigated theoretically. The dynamic resistance of a step is obtained in the limit that the capacitance of the junction is small. The phase fluctuations of the junction are greatly reduced in the presence of the microwave signal, and the dynamic resistance can be extremely small.
The effect of noise on the current-voltage characteristic of a Josephson junction is investigated (1) when the temperature is near the transition temperature of the superconductors and (2) when the junction is driven by an external signal. In case (1) the noise source is the quasiparticle tunneling current but in case (2) there is in addition the noise arising from the finite linewidth of the external signal. This latter noise source is shown to dominate when the junction is operating at high harmonics. We treat the problem in the limits of small and large capacitance and obtain a criterion to determine under what circumstances each limit applies. A solution that includes a first-order correction due to a finite capacitance is given. In the limit of large capacitance the existence and lifetime of hysteresis curves are discussed.
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.
Quantum fluctuations of the charge at a current-biased Josephson junction and of the Josephson current couple to the quasiparticle tunneling when the system is at equilibrium in the zero-voltage state. The effect of reducing the capacitance of the junction is studied by means of a model Hamiltonian. When this becomes smaller, charge fluctuations are reduced, but the effective dissipation is also lowered so that the junction displays an underdamped behavior. The Josephson branch is shifted at the voltage e/2C because of charging due to the quasiparticles. A path-integral formulation of the model leads to a high dynamical subgap resistance at I\ensuremath{\rightarrow}0, as recently found experimentally.
Tl-2212 bicrystal Josephson junctions on SrTiO3 substrates have been fabricated. The I-V characteristic of a Josephson junction under microwave radiation were measured，and microwave induced steps were observed in accordance with the Josephson frequency-voltage relationship. The RCSJ model including noise of bicrystal Josephson junction was constructed through numerical simulation，and the results of simulation were in good agreement with the experimental data. Using the RCSJ model，we investigated the effect of noise on the dynamic characteristics of Josephson junction through simulation，and explained the phenomenon of reduced height and increased breadth of the minima of microwave induced steps. We proposed that the effective noise temperature should be the sum of operational temperature and equivalent temperature of the external noise.
We theoretically investigate the phase and voltage correlation dynamics, which includes both the deterministic contribution and stochastic fluctuations, under a current noise generated by a resistor including thermal and quantum fluctuations in a resistively and capacitively shunted Josephson junction. An external current is found to shift and intensify the deterministic contributions in phase and voltage. In addition to effects of external current, we observe the relaxation of autocorrelation functions of phase and voltage, which includes the variances due to the current noise, to finite values in the long-time limit. In particular, we find that the asymptotic correlations depend on the resistance as a consequence of quantum effects. We also find an earlier decay of coherence at a higher temperature in which thermal fluctuations dominate over quantum ones. These theoretical predictions can be tested in the next future experiments.