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arXiv:cond-mat/0301277

Resonant Cooper-Pair Tunneling: Counting Statistics and Frequency-Dependent Current Noise

A. A. Clerk

Published Jan 15, 2003• 0 citations
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Abstract

We discuss the counting statistics and current noise associated with the double Josephson quasiparticle resonance point in a superconducting single electron transistor. The counting statistics are in general phase-dependent, despite the fact that the average current has no dependence on phase. Focusing on parameter regimes where the counting statistics have no phase-dependence, we use a general relation first derived by MacDonald in 1948 to obtain the full frequency-dependent shot noise directly from the counting statistics, without any further approximations. We comment on problems posed by the phase-dependence of the counting statistics for the finite-frequency noise.

DOI
10.48550/arxiv.cond-mat/0301277

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We discuss the counting statistics and current noise associated with the double Josephson quasiparticle resonance point in a superconducting single electron transistor. The counting statistics are in general phase-dependent, despite the fact that the average current has no dependence on phase. Focusing on parameter regimes where the counting statistics have no phase-dependence, we use a general relation first derived by MacDonald in 1948 to obtain the full frequency-dependent shot noise directly from the counting statistics, without any further approximations. We comment on problems posed by the phase-dependence of the counting statistics for the finite-frequency noise.
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We study intrinsic noise of current in a superconducting single-electron transistor, taking into account both coherence effects and Coulomb interaction near a Cooper pair resonance. Because of this interplay, the statistics of tunneling events deviates from the Poisson distribution and, more important, it shows even-odd asymmetry in the transmitted charge. The zero-frequency noise is suppressed significantly when the quasiparticle tunneling rates are comparable to the coherent oscillation frequency of Cooper pairs.
We analyze charge tunneling statistics and current noise in a superconducting single-electron transistor in a regime where the Josephson-quasiparticle cycle is the dominant mechanism of transport. Due to the interplay between Coulomb blockade and Josephson coherence, the probability distribution for tunneling events strongly deviates from a Poissonian and displays a pronounced even-odd asymmetry in the number of transmitted charges. The interplay between charging and coherence is reflected also in the zero-frequency current noise which is significantly quenched when the quasiparticle tunneling rates are comparable to the coherent Cooper pair oscillation frequency. Furthermore, the finite frequency spectrum shows a strong enhancement near the resonant transition frequency for Josephson tunneling.
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We investigate a superconducting single-electron transistor capacitively coupled to a nanomechanical oscillator and focus on the double Josephson quasiparticle resonance. The existence of two coherent Cooper-pair tunneling events is shown to lead to pronounced back action effects. Measuring the current and the shot noise provides a direct way of gaining information on the state of the oscillator. In addition to an analytical discussion of the linear-response regime, we discuss and compare results of higher-order approximation schemes and a fully numerical solution. We find that cooling of the mechanical resonator is possible and that there are driven and bistable oscillator states at low couplings. Finally, we also discuss the frequency dependence of the charge noise and the current noise of the superconducting single electron transistor.
The form of electron counting statistics of the tunneling current noise in a generic many-body interacting electron system is obtained and universal relations between its different moments are derived. A generalized fluctuation-dissipation theorem providing a relation between current and noise at arbitrary bias-to-temperature ratio eV∕kBTeV∕{k}_{B}TeV∕kB​T is established in the tunneling Hamiltonian approximation. The third correlator of current fluctuations S3{S}_{3}S3​ (the skewness of the charge counting distribution) has a universal Schottky-type relation with the current and quasiparticle charge that holds in a wide bias voltage range, both at large and small eV∕kBTeV∕{k}_{B}TeV∕kB​T. The insensitivity of S3{S}_{3}S3​ to the Nyquist-Schottky crossover represents an advantage compared to the Schottky formula for the noise power. We discuss the possibility of using the correlator S3{S}_{3}S3​ for detecting quasiparticle charge at high temperatures.