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physica status solidi (b)

Response Approach to Current and Noise Power Spectrum of Cooper Pair Tunneling in Ultrasmall Junctions

Wolfram Krech, A. Hädicke

Published Nov 1, 1993• 2 citations
Publisher

Abstract

Abstract Using the response theory approach, the mean current due to tunneling of Cooper pairs in microwave driven superconducting junctions coupled to an electromagnetic environment is derived. The noise power spectrum is calculated showing shot noise behaviour due to the stochastic character of Cooper pair tunneling if the Josephson coupling energy is much smaller than the charging energy.

DOI
10.1002/pssb.2221800116

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arXiv:cond-mat/0209076•Sep 4, 2002•0 citations
Abstract Using the response theory approach, the mean current due to tunneling of Cooper pairs in microwave driven superconducting junctions coupled to an electromagnetic environment is derived. The noise power spectrum is calculated showing shot noise behaviour due to the stochastic character of Cooper pair tunneling if the Josephson coupling energy is much smaller than the charging energy.
The current-voltage characteristics of ultrasmall Josephson junctions sensitively depend on the electromagnetic environment of the junction. When the charging energy exceeds the Josephson coupling energy, the usual supercurrent at zero voltage is completely suppressed. However, for typical environmental impedances, which are small compared to the resistance quantum, stochastic Cooper-pair tunneling leads to a supercurrent peak at a small finite voltage which is proportional to the temperature and the low-frequency resistance of the external circuit. An analytic expression for the form of this universal peak, which is independent of the high-frequency behavior of the environment, is given. With increasing Josephson coupling the peak merges into the usual supercurrent of a Josephson junction. At larger voltages the Cooper-pair current depends on details of the environment. Current peaks are shown to result from resonances in the environmental impedance. Specifically, the case of an LC transmission line of finite length is discussed.
Within a semiclassical approximation and at the weak-coupling limit, where the charging energy dominates the Josephson coupling energy, the dynamics of small-capacitance superconducting tunnel junctions can be described by a stochastic master equation for the probability distribution of junction charges. We develop a method of solving this equation and obtain an analytic solution when Cooper-pair, quasiparticle, and Zener tunneling are all present under an arbitrary Ohmic conductance at zero temperature. We use this solution to systematically investigate the static and dynamic properties of small Josephson junctions. The charge distributions, current-voltage characteristics, and voltage spectra are analytically calculated and numerically evaluated for wide ranges of parameters. The separate contributions from quasiparticle and Cooper-pair tunneling to voltage spectra are evaluated and compared based on their respective sum rules. The linewidths of the resonance peaks for single-electron tunneling and Bloch oscillations are also discussed.
We examine the energy level structure of a Josephson charge qubit (Cooper pair box) coupled to its environment, utilising a backreaction technique originally proposed for characterising persistent current qubits. The system consists of a model charge qubit coupled to three electromagnetic modes: a low frequency bias field, a higher frequency microwave to excite the qubit into higher states, and a lossy reservoir representing the cavity containing the qubit and control fields. Specifically, the qubit is a small superconducting island connected to a bulk superconductor via a weak Josephson junction, allowing Cooper pairs to tunnel on and off the island coherently. The classical bias field experiences a backreaction from the qubit and the noise power increases when the qubit is operating near a transition.
The supercurrent of a Josephson junction is reduced by phase diffusion. For ultrasmall capacitance junctions the current may be further decreased by Coulomb blockade effects. We calculate the Cooper pair current by means of time-dependent perturbation theory to all orders in the Josephson coupling energy and obtain the current-voltage characteristic in closed form in a range of parameters of experimental interest. The results comprehend phase diffusion of the coherent Josephson current in the classical regime as well as the supercurrent peak due to incoherent Cooper pair tunneling in the Coulomb blockade regime.
We have investigated the influence of shot noise on the IV-curves of a single mesoscopic Josephson junction. We find that the blockade of the Cooper pair current is strongly suppressed in the presence of shot noise due to tunnelling in an adjacent SIN junction. Our experimental findings can be accounted for by an extension of the phase correlation theory. Shot-noise effect in a resistive environment R can be characterized by the effective noise temperature T_N = eIR /2 k_B, which means that a Josephson junction can easily detect shot noise from a current well below 1 pA.