Concerning the question of whether we have taken the effects of higher Bloch bands into effect, our numerical calculations do take this into account. The question of higher Bloch bands is a little subtle when it comes to our analytical calculation done in the Wannier-Stark picture. In the presence of the force, the true eigenstates of the system are no longer the Bloch states but the localized Wannier-Stark states. In the analytical calculation we restrict ourselves to just the ground band Wannier-Stark states. However, even with this approximation we find very good agreement between the numerical and analytical calculations.
Also the BEC will lead to an effective change of the cavity length and lattice constant, which should renormalize the wavelength and thus om_recoil.