Effect of quantum noise and tunneling on the fluctuational voltage-current characteristics and the lifetime of the zero-voltage state in Josephson junctions.

Abstract

The minima of the potential energy for the dynamical variable \ensuremath{\varphi} of a Josephson junction are separated by barriers of height \ensuremath{\Elzxh}${I}_{c}$/e, where ${I}_{c}$ is the critical current. At low temperatures, T\ensuremath{\ll}\ensuremath{\Elzxh}${I}_{c}$/e, the time-averaged voltage across the junction has its origin in thermally activated processes, which are more important than quantum tunneling if Tg\ensuremath{\Elzxh}\ensuremath{\Omega}/2\ensuremath{\pi} (\ensuremath{\Omega} is the Josephson plasma frequency). We consider this problem for high-quality junctions (RC\ensuremath{\Omega}\ensuremath{\gg}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 \ensuremath{\varphi} and \ensuremath{\varphi}\ifmmode \dot{}\else \.{}\fi{}, 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 I4${I}_{c}$/\ensuremath{\pi}RC\ensuremath{\Omega}. We discuss the ohmic resistance of the junction, the case of a relatively high damping (1\ensuremath{\ll}RC\ensuremath{\Omega}\ensuremath{\ll}\ensuremath{\Elzxh}${I}_{c}$/T), the classical limit \ensuremath{\Elzxh}\ensuremath{\Omega}/T\ensuremath{\rightarrow}0, and perturbative quantum corrections in (\ensuremath{\Elzxh}\ensuremath{\Omega}/T${)}^{2}$\ensuremath{\ll}1. At currents I\ensuremath{\ll}${I}_{c}$ and I\ensuremath{\gg}${I}_{c}$/RC\ensuremath{\Omega},eT/\ensuremath{\Elzxh} we obtain an expression for the lifetime \ensuremath{\tau} of the zero-voltage state. Numerical results for \ensuremath{\tau} are also presented.