Driven Andreev molecule

Abstract

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