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Journal of Applied Physics

Effect of Noise on the Current-Voltage Characteristics of a Josephson Junction

Patrick A. Lee

Published Jan 1, 1971• 104 citations
Publisher

Abstract

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.

DOI
10.1063/1.1659596

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Physica Scripta•Jun 1, 1982•11 citations
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 investigate the noise-affected I-V curves of small-area Josephson junctions through experiment, simulation, and theory. In particular, we consider I-V curves in which two different states of finite voltage coexist at the same dc bias: a high-voltage state that corresponds to the usual quasiparticle branch and a low-voltage state that is characterized by thermally activated phase diffusion. The observed hysteresis between the phase-diffusion and quasiparticle branches cannot be explained within the context of the simple resistively and capacitively shunted junction (RCSJ) model but is explained by extended models in which the damping increases with frequency. Frequency-dependent damping is shown to produce a qualitative change in the attractors of the noise-free system which allows the two voltage states to be simultaneously stable. This picture is confirmed by Monte Carlo simulations which accurately reproduce the experimental I-V curves of two different samples over a wide range of temperatures. In addition we develop analytic expressions for three key parameters of the I-V curve of junctions displaying hysteresis between the phase-diffusion and quasiparticle branches: the initial slope of the phase-diffusion branch, the bias level at which the junction switches from the phase-diffusion branch to the quasiparticle branch, and the bias level at which it returns to the phase-diffusion branch.
Measurements have been made of the low-frequency spectral density of the voltage noise in current-biased resistively shunted Josephson tunnel junctions under conditions in which the noise mixed-down from frequencies near the Josephson frequency (${\ensuremath{\nu}}_{J}$) to the measurement frequency ($\ensuremath{\ll}{\ensuremath{\nu}}_{J}$) is in the regime $h{\ensuremath{\nu}}_{J}>{k}_{B}T$. In this limit, quantum corrections to the mixed-down noise are important. The spectral densities measured on junctions with current-voltage characteristics close to the Stewart-McCumber model were in excellent agreement with the predicted values, with no fitted parameters. The mixed-down noise for a wide range of bias voltages was used to infer the spectral density of the current noise in the shunt resistor at frequency $\ensuremath{\nu}$. With no fitted parameters, this spectral density at frequencies up to 500 GHz was in excellent agreement with the prediction $(\frac{2h\ensuremath{\nu}}{R})coth(\frac{h\ensuremath{\nu}}{2{k}_{B}T})$. The presence of the zero-point term, $\frac{2h\ensuremath{\nu}}{R}$, at frequencies $h\ensuremath{\nu}>{k}_{B}T$ was clearly demonstrated. The current-voltage characteristics of a junction with ${\ensuremath{\beta}}_{L}\ensuremath{\equiv}\frac{2\ensuremath{\pi}{L}_{s}{I}_{0}}{{\ensuremath{\Phi}}_{0}}\ensuremath{\sim}1$ and ${\ensuremath{\beta}}_{C}\ensuremath{\equiv}\frac{2\ensuremath{\pi}{I}_{0}{R}^{2}C}{{\ensuremath{\Phi}}_{0}}\ensuremath{\ll}1$, where I0{I}_{0}I0​ is the critical current, CCC is the junction capacitance, and Ls{L}_{s}Ls​ is the shunt inductance, showed structure at voltages where the Josephson frequency was near a subharmonic of the LsC{L}_{s}CLs​C resonant frequency. The additional nonlinearity of the $I\ensuremath{-}V$ characteristic caused mixing down of noise near higher harmonics of the Josephson frequency, thereby greatly enhancing the voltage noise. The measured noise was in good agreement with that predicted by computer simulations.
We measure current fluctuations of mesoscopic devices in the quantum regime, when the frequency is of the order of or higher than the applied voltage or temperature. Detection is designed to probe separately the absorption and emission contributions of current fluctuations, i.e. the positive and negative frequencies of the Fourier transformed nonsymmetrized noise correlator. It relies on measuring the quasiparticles photon assisted tunneling current across a superconductor-insulator-superconductor junction (the detector junction) caused by the excess current fluctuations generated by quasiparticles tunneling across a Josephson junction (the source junction). We demonstrate unambiguously that the negative and positive frequency parts of the nonsymmetrized noise correlator are separately detected and that the excess current fluctuations of a voltage biased Josephson junction present a strong asymmetry between emission and absorption.
Relaxation oscillations at subharmonics of the Josephson frequency may occur in a resistively shunted superconducting tunnel junction, where the shunt loop has a large inductance. We have studied the variation in the relaxation period with the shunt inductance and resistance, the Josephson critical current, and the bias current. Steps in the current-voltage curve were noted at bias points where the subharmonic number changed. Radiation powers of the order of a nW were coupled out of small, single, tunnel junctions at 10 GHz. Linewidths scaled with the frequency square as compared with those of the Josephson mode oscillations. Wide signals centered around harmonics of the relaxation frequency were due to amplified noise. Injection locking to a fraction of the frequency of a relatively strong signal occurred, while weaker signals were amplified. Gains up to 15 dB were achieved within a fairly large bandwidth, but the noise temperature was high. The importance of parametrically up-converted noise from low idler frequencies is emphasized.