  Here we present a theoretical investigation of the Floquet spectrum in
multiterminal quantum dot Josephson junctions biased with commensurate
voltages. We first draw an analogy between the electronic band theory and
superconductivity which enlightens the time-periodic dynamics of the Andreev
bound states. We then show that the equivalent of the Wannier-Stark ladders
observed in semiconducting superlattices via photocurrent measurements, appears
as specific peaks in the finite frequency current fluctuations of
superconducting multiterminal quantum dots. In order to probe the
Floquet-Wannier-Stark ladder spectra, we have developed an analytical model
relying on the sharpness of the resonances. The charge-charge correlation
function is obtained as a factorized form of the Floquet wave-function on the
dot and the superconducting reservoir populations. We confirm these findings by
Keldysh Green's function calculations, in particular regarding the voltage and
frequency dependence of the resonance peaks in the current-current
correlations. Our results open up a road-map to quantum correlations and
coherence in the Floquet dynamics of superconducting devices.

Mesoscale and Nanoscale Physics;Superconductivity