Non-perturbative theoretical description of two atoms in an optical   lattice with time-dependent perturbations
  A theoretical approach for a non-perturbative dynamical description of two interacting atoms in an optical lattice potential is introduced. The approach builds upon the stationary eigenstates found by a procedure described in Grishkevich et al. [Phys. Rev. A 84, 062710 (2011)]. It allows presently to treat any time-dependent external perturbation of the lattice potential up to quadratic order. Example calculations of the experimentally relevant cases of an acceleration of the lattice and the turning-on of an additional harmonic confinement are presented. 
Philipp-Immanuel Schneider and Sergey Grishkevich and Alejandro Saenz
cond-mat.quant-gas quant-ph