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Physica B Condensed Matter

Suppression of the Josephson current by quantum phase fluctuations: beyond the adiabatic approximation

Ulrich Geigenmüller, Masahito Ueda

Published Feb 1, 1994• 0 citations
Publisher
DOI
10.1016/0921-4526(94)90832-x

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Quantum fluctuations in a current-biased Josephson junction, described in terms of the RCSJ model, are considered. The fluctuations of the voltage and phase across the junction are assumed to be initiated by equilibrium current fluctuations in the shunting resistor. This corresponds to low enough temperatures, when fluctuations of the normal current in the junction itself can be neglected. We used the quantum Langevin equation in terms of random variables related to the limit cycle of the nonlinear Josephson oscillator. This allows to go beyond the perturbation theory and to calculate the widths of the Josephson radiation lines.
We consider quantum fluctuations in a current biased overdamped Josephson junction in the regime when the bias current is larger than the critical current. The fluctuations of the voltage and phase across the junction are assumed to be initiated by equilibrium current fluctuations in the shunting resistor. This corresponds to low enough temperatures, when fluctuations of the normal current in the junction itself can be neglected. Quantum effects are important when the resistor temperature is low compared to the Josephson frequency, even in the case when noise is measured at frequencies lower than the temperature. We used the quantum Langevin equation in terms of random variables related to the limit cycle of the nonlinear Josephson oscillator. This allows to go beyond the perturbation theory and calculate the widths of the Josephson radiation lines.
We study the relation between the models commonly used to describe the dynamics of nonresonantly pumped exciton-polariton condensates, namely the ones described by the complex Ginzburg-Landau equation, and by the open-dissipative Gross-Pitaevskii equation including a separate equation for the reservoir density. In particular, we focus on the validity of the adiabatic approximation and small density fluctuations approximation that allow one to reduce the coupled condensate-reservoir dynamics to a single partial differential equation. We find that the adiabatic approximation consists of three independent analytical conditions that have to be fulfilled simultaneously. By investigating stochastic versions of the two corresponding models, we verify that the breakdown of these approximations can lead to discrepancies in correlation lengths and distributions of fluctuations. Additionally, we consider the phase diffusion and number fluctuations of a condensate in a box, and show that self-consistent description requires treatment beyond the typical Bogoliubov approximation.