Charging ultrasmall tunnel junctions in an electromagnetic environment

We have investigated the quantum admittance of an ultrasmall tunnel junction with arbitrary tunneling strength under an electromagnetic environment. Using the functional-integral approach a close analytical expression of the quantum admittance is derived for a general electromagnetic environment. We then consider a specific controllable environment where a resistance is connected in series with the tunneling junction, for which we derived the de quantum conductance from the zero-frequency limit of the imaginary part of the quantum admittance. For such an electromagnetic environment the de conductance has been investigated in recent experiments, and our numerical results agree quantitatively very well with the measurements. Our complete numerical results for the entire range of junction conductance and electromagnetic environmental conductance confirmed the few existing theoretical conclusions.