Abstract
The interaction of a mesoscopic Josephson junction with superposition of even and odd coherent states is investigated. It is found that the expectation value and the fluctuation of a supercurrent can exhibit dc components. The number of current-voltage steps (CVSs) for the former are less than the latter. For the former the static supercurrent flows in a positive or negative direction, which depends on the phase of the light field. The correlation function and squeezing of the dc components of a supercurrent depend on the value of CVS. For some special value of a CVS, the squeezing disappears.