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Stochastic dynamics of a Josephson junction threshold detector.

Eugene V Sukhorukov1, Andrew N Jordan

  • 1Départment de Physique Théorique, Université de Genève, CH-1211 Genève 4, Switzerland.

Physical Review Letters
|May 16, 2007
PubMed
Summary

We generalized stochastic path integrals for systems with general Markovian noise. This allows calculating activation rates for non-Gaussian noise, with applications to Josephson junction detectors and electron counting statistics.

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Area of Science:

  • Theoretical Physics
  • Quantum Optics
  • Condensed Matter Physics

Background:

  • Stochastic path integral formalism is crucial for describing quantum systems with dissipation.
  • Kramers' solution provides a method for calculating escape rates over potential barriers.
  • Josephson junction detectors are vital for precise measurements in mesoscopic systems.

Purpose of the Study:

  • To generalize the stochastic path integral formalism to include general Markovian noise.
  • To extend Kramers' solution for activation rates to non-Gaussian driving noise.
  • To apply these generalized methods to a Josephson junction detector for electron counting statistics.

Main Methods:

  • Generalization of the stochastic path integral formalism.
  • Derivation of activation rates for both overdamped and underdamped limits with non-Gaussian noise.
  • Application to a Josephson junction system for analyzing measurement backaction.

Main Results:

  • A generalized Kramers' solution applicable to non-Gaussian noise.
  • The derived activation rate explicitly depends on the third current cumulant.
  • Identification of an additional term in the activation rate due to measurement circuit backaction.

Conclusions:

  • The study provides a robust theoretical framework for analyzing systems with general Markovian noise.
  • The findings offer new insights into the dynamics of Josephson junction detectors and electron counting.
  • The work highlights the importance of considering measurement backaction in quantum transport phenomena.