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

V. I. Mel’nikov; A. Sütö

doi:10.1103/PhysRevB.34.1514

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

V. I. Mel’nikov, A. Sütö

DOI 10.1103/PhysRevB.34.1514 · Physical Review B

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Abstract

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 φ̇, 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.