Done. We have re-written the first part of the abstract as: “In this paper we give a new description, in terms of optomechanics, of previous work on the problem of an atomic Bose-Einstein condensate interacting with the optical lattice inside a laser-pumped optical cavity and subject to a bias force such as gravity \cite{Ven09,Ped09,Gol14}. An atomic wave packet in a tilted lattice undergoes Bloch oscillations; in a highfinesse optical cavity the backaction of the atoms on the light leads to a time-dependent modulation of the intracavity lattice depth at the Bloch frequency which can in turn transport the atoms up or down the lattice.”
(1) It should be somehow mentioned more clearly (maybe in the abstract) that the idea is not completely new but work presents a new and more intutive picture of the system dynamics.