TRANSFER-ENERGY-DEPENDENT ESCAPE RATE OF ELECTRONS THROUGH A SMALL-CAPACITANCE TUNNEL JUNCTION

The dynamics of a tunneling electron through a small-capacitance tunnel junction are studied by developing a method for self-consistently determining escape rate and barrier traversal time for those electrons that transfer a given energy to the electromagnetic environment. The transfer-energy-dependent escape rate lets us examine dissipative and nondissipative tunneling rates separately and its integral over the transfer energy gives the total escape rate that is obtained by the instanton technique. It is found that the escape rate increases exponentially with increasing the ratio of the elementary charging energy to the quantized energy of the environment, but that the traversal time peaks at one particular ratio. As the frequency of the electromagnetic mode increases, an effective potential is shown to change from linear (dominated by the zero-point fluctuations of charge on the junction) to parabolic (dominated by the static polarization of the charge). Possible experimental situations for observing the predicted effects are discussed.