Quantum fluctuations and charging effects in small tunnel junctions

The finite voltage conductance of an ultrasmall single tunnel junction of nominal resistance ${\mathit{R}}_0$ is calculated within a model that includes quantum voltage fluctuations. Fluctuations are induced by charge transfer across the junction as well as by coupling to its electromagnetic environment via a transmission line of arbitrary impedance Z(ω). Both types of quantum fluctuations suppress the Coulomb blockade. Within a harmonic approximation we show that for a general frequency-dependent transmission-line impedance the impedances simply add in parallel. The low-frequency fluctuations are given by an effective coupling constant ${\gamma }_{\mathrm{tot}}$=${\mathit{R}}_{\mathit{H}}$/2${\mathit{Z}}_{\mathrm{tot}}$, where ${\mathit{Z}}_{\mathrm{tot}}^{\mathrm{-}1}$=Z(0${)}^{\mathrm{-}1}$+${\mathit{R}}_0^{\mathrm{-}1}$ and ${\mathit{R}}_{\mathit{H}}$=h/${\mathit{e}}^2$ is the quantum of resistance.