Fractional photon-assisted tunnelling of ultra-cold atoms in periodically shaken double-well lattices

Fractional photon-assisted tunnelling is investigated both numerically and analytically in a double-well lattice. While integer photon-assisted tunnelling is a single-particle effect, fractional photon-assisted tunnelling is an interaction-induced many-body effect. Double-well lattices with few particles in each double well are ideal to study this effect far from the mean-field effects. It is predicted that the 1/4-resonance is observable in such systems. Fractional photon-assisted tunnelling provides a physically relevant model for which N-th order time-dependent perturbation theory can be large although all previous orders are small.