Effect of quantum noise and tunneling on the fluctuational voltage-current characteristics and the lifetime of the zero-voltage state in Josephson junctions
The minima of the potential energy for the dynamical variable φ of a Josephson junction are separated by barriers of height ħIc/e, where Ic is the critical current. At low temperatures, T<<ħIc/e, the time-averaged 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 high-quality junctions (RCΩ>>1, R and C are the resistance and the capacitance of the junction), accounting for the effect of a Johnson-Nyquist 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 steady-state distribution of φ and φ˙, and solve it by a modification of the Wiener-Hopf method. The result is a formula for the current dependence of the fluctuational voltage, valid for currents I<4Ic/πRCΩ. We discuss the ohmic resistance of the junction, the case of a relatively high damping (1<<RCΩ<<ħIc/T), the classical limit ħΩ/T-->0, and perturbative quantum corrections in (ħΩ/T)2<<1. At currents I<<Ic and I>>Ic/RCΩ,eT/ħ we obtain an expression for the lifetime τ of the zero-voltage state. Numerical results for τ are also presented.
Physical Review B
- Pub Date:
- August 1986
- Tunneling phenomena;
- point contacts weak links Josephson effects