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Here we present a theoretical investigation of the Floquet spectrum inmultiterminal quantum dot Josephson junctions biased with commensuratevoltages. We first draw an analogy between the electronic band theory andsuperconductivity which enlightens the time-periodic dynamics of the Andreevbound states. We then show that the equivalent of the Wannier-Stark laddersobserved in semiconducting superlattices via photocurrent measurements, appearsas specific peaks in the finite frequency current fluctuations ofsuperconducting multiterminal quantum dots. In order to probe theFloquet-Wannier-Stark ladder spectra, we have developed an analytical modelrelying on the sharpness of the resonances. The charge-charge correlationfunction is obtained as a factorized form of the Floquet wave-function on thedot and the superconducting reservoir populations. We confirm these findings byKeldysh Green's function calculations, in particular regarding the voltage andfrequency dependence of the resonance peaks in the current-currentcorrelations. Our results open up a road-map to quantum correlations andcoherence in the Floquet dynamics of superconducting devices.

Engineering the Floquet spectrum of superconducting multiterminal quantum dots