Effect of quantum noise and tunneling on the fluctuational voltagecurrent characteristics and the lifetime of the zerovoltage state in Josephson junctions
Abstract
The minima of the potential energy for the dynamical variable φ of a Josephson junction are separated by barriers of height ħI_{c}/e, where I_{c} is the critical current. At low temperatures, T<<ħI_{c}/e, the timeaveraged voltage across the junction has its origin in thermally activated processes, which are more important than quantum tunneling if T>ħΩ/2π (Ω is the Josephson plasma frequency). We consider this problem for highquality junctions (RCΩ>>1, R and C are the resistance and the capacitance of the junction), accounting for the effect of a JohnsonNyquist noise and quantum tunneling at the barrier top. With a simplifying assumption, we derive a pair of integral equations containing an energy variable for the steadystate distribution of φ and φ˙, and solve it by a modification of the WienerHopf method. The result is a formula for the current dependence of the fluctuational voltage, valid for currents I<4I_{c}/πRCΩ. We discuss the ohmic resistance of the junction, the case of a relatively high damping (1<<RCΩ<<ħI_{c}/T), the classical limit ħΩ/T>0, and perturbative quantum corrections in (ħΩ/T)^{2}<<1. At currents I<<I_{c} and I>>I_{c}/RCΩ,eT/ħ we obtain an expression for the lifetime τ of the zerovoltage state. Numerical results for τ are also presented.
 Publication:

Physical Review B
 Pub Date:
 August 1986
 DOI:
 10.1103/PhysRevB.34.1514
 Bibcode:
 1986PhRvB..34.1514M
 Keywords:

 05.40.+j;
 74.50.+r;
 Tunneling phenomena;
 point contacts weak links Josephson effects