Forming doublons by a quantum quench

Repulsive interactions between particles on a lattice may lead to bound states, so called doublons. Such states may be created by dynamically tuning the interaction strength, e.g. using a Feshbach resonance, from attraction to repulsion. We study the doublon production efficiency as a function of the tuning rate at which the on-site interaction is varied. An expectation based on the Landau-Zener law suggests that exponentially few doublons are created in the adiabatic limit. Contrary to such an expectation, we found that the number of produced doublons scales as a power law of the tuning rate with the exponent dependent on the dimensionality of the lattice. The physical reason for this anomaly is the effective decoupling of doublons from the two-particle continuum for center-of-mass momenta close to the corners of the Brillouin zone. The study of doublon production may be a sensitive tool to extract detailed information about the band structure.