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arXiv:cond-mat/9511128 · Physical Review Letters

Supercurrent Noise in Quantum Point Contacts

D. V. Averin, H. T. Imam

Published May 13, 1996• 106 citations
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Abstract

Spectral density of current fluctuations in a short ballistic superconducting quantum point contact is calculated for arbitrary bias voltages $V$. Contrary to a commonly held view that the supercurrent flow in Josephson junctions is a coherent process without fluctuations, we find extremely large current noise that is caused by the supercurrent coherence. At finite voltages, this noise can be qualitatively understood as the shot noise of the large charge quanta of magnitude $2\ensuremath{\Delta}/V$ equal to the charge transferred through the contact during one period of the Josephson oscillations.

DOI
10.1103/physrevlett.76.3814

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Spectral density of current fluctuations in a short ballistic superconducting quantum point contact is calculated for arbitrary bias voltages VVV. Contrary to a commonly held view that the supercurrent flow in Josephson junctions is a coherent process without fluctuations, we find extremely large current noise that is caused by the supercurrent coherence. At finite voltages, this noise can be qualitatively understood as the shot noise of the large charge quanta of magnitude 2\ensuremathΔ/V2\ensuremath{\Delta}/V2\ensuremathΔ/V equal to the charge transferred through the contact during one period of the Josephson oscillations.
We analyze the shot noise in a voltage biased superconducting quantum point contact. Results are presented for the single channel case with arbitrary transmission. In the limit of very low transmission it is found that the effective charge, defined from the noise-current ratio, exhibits a steplike behavior as a function of voltage with well-defined plateaus at integer values of the electronic charge. This multiple charge corresponds to the transmitted charge in a multiple Andreev reflection (MAR) process. This effect gradually disappears for increasing transmission due to interference between different MAR processes.
Josephson junctions are dissipationless elements used notably in superconducting nanocircuits. While being indispensable for the making of superconducting quantum bits, they are plagued by intrinsic noise mechanisms that reduce the coherence time of the quantum devices. An important source of such fluctuations may come from the non-cristallinity and disorder of the oxide layer sandwiched between the two superconducting leads. \nIn this work, roughness in a Josephson junction is modeled as a set of pinholes with a universal bimodal distribution of transmission eigenvalues that sum incoherently in the noise power. Each of these channels is treated as a ballistic quantum point contact with a thin barrier that determines the transmission eigenvalue. The noise spectrum is calculated using the quasiclassical Green's function method to analyze high and low transmission limits at non-zero temperature for all interesting frequencies. As suggested by experiments, low transmission channels generate shot noise while fast switching between subgap states creates strong non-poissonian low-frequency noise. However, when analyzed for three different universal models of disorder, the principal contribution to noise is found to come from the partially opened channels. Finally, fluctuations of the noise from sample to sample is seen to be dominated by the contribution of opened channels which may reduce the reproducibility of results between different experiments.
We report measurements of the white noise in superconducting niobium point contacts. These measurements, the junction parameters, and the method of fabrication of the point contacts are compared with those of other experiments. The power spectral density was found to have an approximately parabolic dependence on the average voltage V rather than the linear dependence expected in the shot-noise limit. We also found that the magnitude of the excess noise was larger than has been previously reported. Because of these differences, the noise data presented add to the existing body of data. The V2 dependence of the power spectral density suggests that Joule heating may have been responsible for the excess noise. Joule heating was determined to be present in the junctions from the relatively small critical currents I0 ≲2 μA and the effect that a resonant cavity had on the Josephson oscillation. However, we show that Joule heating cannot account for the level of the excess noise observed in present or previous data.
Critical current fluctuations with a 1∕f spectral density (f is frequency) are potentially a limiting source of intrinsic decoherence in superconducting quantum bits (qubits) based on Josephson tunnel junctions. Prior measurements of this noise were made at nonzero voltages whereas qubits are operated in the zero voltage state. We report measurements of 1∕f noise in a dc superconducting quantum interference device first, coupled to a resonant tank circuit and operated in a dispersive mode at zero voltage, and, second, operated conventionally with a current bias in the voltage regime. Both measurements yield essentially the same magnitude of critical current 1∕f noise.
We develop a theory of Coulomb oscillations in superconducting devices in the limit of small charging energy EC≪ΔE_C \ll ΔEC​≪Δ. We consider a small superconducting grain of finite capacity connected to two superconducting leads by nearly ballistic single-channel quantum point contacts. The temperature is supposed to be very low, so there are no single-particle excitations on the grain. Then the behavior of the system may be described as quantum mechanics of the superconducting phase on the island. The Josephson energy as a function of this phase has two minima which become degenerate at the phase difference on the leads equal to πππ, the tunneling amplitude between them being controlled by the gate voltage at the grain. We find the Josephson current and its low-frequency fluctuations and predict their periodic dependence on the induced charge Qx=CVgQ_x=C V_gQx​=CVg​ with period 2e2e2e.
We develop a theory of Coulomb oscillations in superconducting devices in the limit of small charging energy E C ≪Δ. We consider a small superconducting grain with finite capacitance connected to two superconducting leads by nearly ballistic single-channel quantum point contacts. The temperature is assumed to be very low, so there are no single-particle excitations on the grain. Then the behavior of the system can be described in terms of the quantum mechanics of the superconducting phase on the island. The Josephson energy as a function of this phase has two minima that become degenerate when the phase difference on the leads equals to π, the tunneling amplitude between them being controlled by the gate voltage on the grain. We find the Josephson current and its low-frequency fluctuations, and predict their periodic dependence with period 2e on the induced charge Q x =CV g .