Semiclassical theory of small Josephson junctions: Solution of the master equation

Akira Furusaki; Masahito Ueda

doi:10.1103/PhysRevB.45.10576

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Semiclassical theory of small Josephson junctions: Solution of the master equation

Akira Furusaki, Masahito Ueda

DOI 10.1103/PhysRevB.45.10576 · Physical Review B

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Abstract

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.