Self-consistent dynamics of a Josephson junction in presence of an arbitrary environment

Abstract

We derive microscopically the dynamics associated with the d.c. Josephson effect in a superconducting tunnel junction interacting with an arbitrary electromagnetic environment. To do so, we extend to superconducting junctions the so-called P(E) theory (see e.g. Ingold and Nazarov, arXiv:cond-mat/0508728) that accurately describes the interaction of a nonsuperconducting tunnel junction with its environment. We show the dynamics of this system is described by a small set of coupled correlation functions that take into account both Cooper pair and quasiparticle tunneling. When the phase fluctuations are small the problem is fully solved self-consistently, using and providing the exact linear admittance Y(ω) of the interacting junction.

7 pages, 1 figure

References in corpus (5)

• Implementation of low-loss superinductances for quantum circuits
• Quasiparticle relaxation of superconducting qubits in the presence of flux
• Counting statistics of transport through Coulomb blockade nanostructures: High-order cumulants and non-Markovian effects
• Quantum Superinductor with Tunable Non-Linearity
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• Rescaling of Applied Oscillating Voltages in Small Josephson Junctions
• Absence of a dissipative quantum phase transition in Josephson junctions: Theory