Resonant tunneling in small current-biased Josephson junctions

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Abstract
We investigate the theory of resonant tunneling of the phase difference φ in current-biased, small-capacitance Josephson junctions. Tunneling of φ occurs between states localized in adjacent wells of the tilted cosine (‘‘washboard’’) potential when the states are nearly degenerate, and leads to unique junction behavior. Most notable are the presence of voltage spikes along the supercurrent branch of the current-voltage characteristic, the reduction of the bias current at which the junction switches to the free-running state to a value well below the thermodynamic value, and peaks in the distribution of rates at which this switching occurs as a function of bias current. For a range of junction parameters, we estimate the magnitude and width of the first (lowest bias current) voltage spike and the rate of switching to the free-running state in the zero temperature, low damping limit. Experimentally, the most readily observable signature of resonant tunneling should be the characteristic peaks in the switching distribution.