Single-particle localization in dynamical potentials

Single particle localization of an ultra-cold atom is studied in one dimension when the atom is confined by an optical lattice and by the incommensurate potential of a high-finesse optical cavity. In the strong coupling regime the atom is a dynamical refractive medium, the cavity resonance depends on the atomic position within the standing-wave mode and nonlinearly determines the depth and form of the incommensurate potential. We show that the particular form of the quasi-random cavity potential leads to the appearance of mobility edges, even in presence of nearest-neighbour hopping. We provide a detailed characterization of the system as a function of its parameters and in particular of the strength of the atom-cavity coupling, which controls the functional form of the cavity potential. For strong atom-photon coupling the properties of the mobility edges significantly depend on the ratio between the periodicities of the confining optical lattice and of the cavity field.