Mesoscopic Josephson junctions in the presence of nonclassical electromagnetic fields

Circular superconducting devices with mesoscopic Josephson junctions are considered in the presence of a dc voltage bias V₀ and of nonclassical electromagnetic fields. It is shown that when the voltage V₀ is an integer multiple of a certain value, the current through the junction has a dc component. This is broadly similar to Shapiro steps in macroscopic Josephson junctions, but the details depend on the nature of the nonclassical electromagnetic field. Coherent states, squeezed states, and number eigenstates are considered and the corresponding Shapiro steps are studied in detail. The presence of thermal noise in the nonclassical fields is also considered and its effect on the results is studied.