Driven Andreev molecule

We study the voltage-biased S-QD-S-QD-S Josephson junction, composed of three superconductors (S) and two quantum dots (QDs). In absence an applied voltage, Andreev bound states on each dot hybridize, forming ``Andreev molecule.'' However, understanding this system in a nonequilibrium setup is lacking. Applying commensurate dc voltages bijunction makes time periodic, equilibrium evolve into ladder resonances with finite lifetime due to multiple reflections (MARs). Starting from time-periodic Bogoliubov--de Gennes equations we map problem tight-binding chain Floquet space. The resolvent non-Hermitian block matrix obtained via continued fraction method. numerically calculate Floquet-Andreev spectra which could be probed by local tunneling spectroscopy dots. also consider subgap current, show that determine position MAR steps. Proximity causes splitting steps, while at large distances observe interference effects cause oscillations current-voltage curves. latter effect should persist very long distances.