Two mesoscopic Josephson junctions in the quantized light fields

The supercurrents in two mesoscopic Josephson junctions in the presence of the quantized light fields are studied. The states of the light fields discussed in this paper include squeezed coherent states, thermal states, even and odd coherent states. The Shapiro dc currents and the even-order fluctuations of supercurrents are discussed. The effects of the field states on the supercurrents are investigated. Interfering between the supercurrents in two junctions in time domain transforms the frequency modulating in single junction into the amplitude modulating in two junctions and forms beats. The modulating degree of amplitude depends on the states of the quantized light fields. The voltage jumps of Shapiro steps in two junctions for the squeezed coherent states and displaced thermal states are double in size in comparison with those in single junction. The fluctuations of supercurrents in two junctions are much larger than those in single junction, but the fundamental quantum fluctuations are zero. The higher-order fluctuations are larger than the lower-order fluctuations. The fluctuations exhibit oscillations with same frequency for each even order and their amplitudes are modulated synchronously.