Reply to "comment on 'coupled dynamics of atoms and radiation-pressure-driven interferometers' and 'superstrong coupling regime of cavity quantum electrodynamics'"

In their Comment, Asbóth and Domokos question the consistency of two approximations introduced in two recent articles. They show that the minimization of the atomic dipole potential does not in general give rise to a regular lattice of ultracold atoms and that the steady-state positions of atoms in a cavity are not normally characterized by a minimum of the dipole potential. Instead, the steady-state positions correspond to a vanishing force on each individual atom, the relevant force being proportional to the derivative of the optical field mode function. We agree with Asbóth and Domokos that the atomic lattice should be irregular. Using a microscopic model we show however that in the regime considered in our works and also in the preceding Comment the concept of force is generally not well defined, and a semiclassical theory may be inadequate for the description of the atomic motion.