Nonequilibrium Fractional Josephson Effect

Josephson tunnel junctions exhibit a supercurrent typically proportional to the sine of the super-conducting phase difference phi. In general, a term proportional to coso phi thorn is also present, alongside microscopic electronic retardation effects. We show that voltage pulses sharply varying in time prompt a significant impact of the coso phi thorn term. Its interplay with the sino phi thorn term results in a nonequilibrium fractional Josephson effect (NFJE) similar to sino phi=2 thorn in the presence of bound states close to zero frequency. Our microscopic analysis reveals that the interference of nonequilibrium virtual quasiparticle excitations is responsible for this phenomenon. We also analyze this phenomenon for topological Josephson junctions with Majorana bound states. Remarkably, the NFJE is independent of the ground state fermion parity unlike its equilibrium counterpart.