Volume 80, Number 1, October 2007
Article Number 17009
Number of page(s) 5
Section Condensed Matter: Electronic Structure, Electrical, Magnetic and Optical Properties
Published online 17 September 2007
EPL, 80 (2007) 17009
DOI: 10.1209/0295-5075/80/17009

Why macroscopic quantum tunnelling in Josephson junctions differs from tunnelling of a quantum particle

A. O. Sboychakov1, 2, Sergey Savel'ev1, 3, A. L. Rakhmanov1, 2, 3 and Franco Nori1, 4

1  Frontier Research System, The Institute of Physical and Chemical Research (RIKEN) - Wako-shi, Saitama, 351-0198, Japan
2  Institute for Theoretical and Applied Electrodynamics Russian Academy of Sciences - 125412 Moscow, Russia
3  Department of Physics, Loughborough University - Loughborough LE11 3TU, UK
4  MCTP, CSCS, Department of Physics, University of Michigan - Ann Arbor, MI 48109-1040, USA

received 14 June 2007; accepted in final form 17 August 2007; published October 2007
published online 17 September 2007

We show that the macroscopic quantum tunnelling of a fluxon in a Josephson junction cannot be described, even qualitatively, as the tunnelling of a quantum particle in a potential $U(\varphi)$, where the phase difference $\varphi$ plays the role of particle position, if the length of the junction d exceeds a fluxon length. We calculate the probability per unit time of tunnelling (or escape rate), $\Gamma $, which has a form $\Gamma $ = A exp (-B). In contrast to particles, where the B is proportional to d, our field-theory predicts a different behavior of B for either usual, 0-$\pi $, or stacks of Josephson junctions, giving rise to a renormalization of $\Gamma $ by many orders of magnitude.

74.50.+r - Tunneling phenomena; point contacts, weak links, Josephson effects.

© Europhysics Letters Association 2007