Anomalous Josephson current through a driven double quantum dot

Josephson junctions based on quantum dots offer a convenient tunability by means of local gates. Here we analyze a Josephson junction based on a serial double quantum dot in which the two dots are individually gated by phase-shifted microwave tones of equal frequency. We calculate the time-averaged current across the junction and determine how the phase shift between the drives modifies the current-phase relation of the junction. Breaking particle-hole symmetry on the dots is found to give rise to a finite average anomalous Josephson current with phase bias between the superconductors fixed to zero. This microwave gated weak link thus realizes a tunable "Floquet φ0 junction"with maximum critical current achieved for driving frequencies slightly off resonance with the subgap excitation energy. We provide numerical results supported by an analytical analysis for infinite superconducting gap and weak interdot coupling. We identify an interaction-driven 0-π transition of anomalous Josephson current as a function of driving phase difference. Finally, we show that this junction can be tuned so as to provide for complete rectification of the time-averaged Josephson current-phase relation.