Quantum phase expectation values of a mesoscopic Josephson junction from quantum current measurements

A simple way to acquire information on the mean values of the phase operators sin phi and cos phi of an ultrasmall Josephson junction prepared in an arbitrary pure or not state is reported. Our proposal exploits the recently predicted occurrence of current spikes in the I-V characteristic of a mesojunction irradiated by a quantum single-mode low-intensity coherent electromagnetic field. A necessary condition for the validity of our treatment is presented and discussed.