Resonant tunneling in small current-biased Josephson junctions.

Abstract

We investigate the theory of resonant tunneling of the phase difference \ensuremath{\varphi} in current-biased, small-capacitance Josephson junctions. Tunneling of \ensuremath{\varphi} 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.