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Physics Letters A

Effect of external circuit on the charge dynamics of ultrasmall Josephson junctions

Dmitry S. Golubev, Andrei D. Zaikin

Published Sep 1, 1990• 7 citations
Publisher
DOI
10.1016/0375-9601(90)90503-g

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Quantum Dynamics of Phase and Charge in Josephson Junctions

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This chapter provides an analysis of macroscopic quantum dynamics of small-size Josephson junctions. It demonstrates that nontrivial interplay between quantum coherence, dissipation, and Coulomb effects yields a rich variety of properties, which can be accessed not only by means of the phase variable but also through the canonically conjugate quantum variable of the junction charge. The chapter argues that useful and sometimes complementary information can be obtained if one considers quantum dynamics of another collective variable—the junction charge. It discusses some (quasi-) equilibrium properties of ultrasmall Josephson junctions, which can be adequately accounted for by evaluating the grand partition function Z within the imaginary-time path integral formalism. In general, however, the imaginary-time technique may be insufficient and/or inconvenient to properly describe real-time evolution of Josephson junctions in the presence of macroscopic quantum coherence and dissipation.

•May 24, 2019•0 citations
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.
This chapter provides an analysis of macroscopic quantum dynamics of small-size Josephson junctions. It demonstrates that nontrivial interplay between quantum coherence, dissipation, and Coulomb effects yields a rich variety of properties, which can be accessed not only by means of the phase variable but also through the canonically conjugate quantum variable of the junction charge. The chapter argues that useful and sometimes complementary information can be obtained if one considers quantum dynamics of another collective variable—the junction charge. It discusses some (quasi-) equilibrium properties of ultrasmall Josephson junctions, which can be adequately accounted for by evaluating the grand partition function Z within the imaginary-time path integral formalism. In general, however, the imaginary-time technique may be insufficient and/or inconvenient to properly describe real-time evolution of Josephson junctions in the presence of macroscopic quantum coherence and dissipation.