Three superconductors contacted within a narrow region form a three-terminal Josephson junction, controlled by two independent voltages, and by two independent phase differences. Coherent DC multipair currents can flow at resonance, for commensurate voltage bias values [1,2]. A simple physical picture of the steady state will be developed , using Floquet theory. The later will be introduced on the example of a driven qu-bit, starting from the rotating wave approximation, and going beyond with Floquet theory. The equilibrium Andreev bound states (for V=0) evolve into nonequilibrium Floquet-Wannier-Stark-Andreev (FWS-Andreev) ladders of resonances (for non-zero V). Those resonances acquire a finite width due to multiple Andreev reflection processes. The effect of an extrinsic line-width broadening on the quantum dot will also be considered, and introduced through a Dynes phenomenological parameter. The dc-quartet current manifests a crossover between the extrinsic relaxation dominated regime at low voltage to an intrinsic relaxation due to MAR processes at higher voltage. Three important low-energy scales will be identified, and a perspective is to relate those low-energy scales to the cross-correlation experiment of the Weizmann group [4,5].
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