Nonadiabatic Josephson current pumping by chiral microwave irradiation

Irradiating a Josephson junction with microwaves can operate not only on the amplitude but also on the phase of the Josephson current. This requires breaking time-inversion symmetry, which is achieved by introducing a phase lapse between the microwave components acting on the two sides of the junction. General symmetry arguments and the solution of a specific single-level quantum dot model show that this induces chirality in the Cooper pair dynamics due to the topology of the Andreev bound-state wave function. Another essential condition is to break electron-hole symmetry within the junction. A shift of the current-phase relation is obtained, which is controllable in sign and amplitude with the microwave phase and an electrostatic gate, thus producing a ``chiral'' Josephson transistor. The dot model is solved in the infinite-gap limit by Floquet theory and in the general case with Keldysh nonequilibrium Green's functions. The chiral current is nonadiabatic: it is extremal and changes sign close to resonant chiral transitions between the Andreev bound states.