Cavity-induced switching between localized and extended states in a non-interacting Bose-Einstein condensate

We study an ultracold atom-cavity coupling system, which had been implemented in experiment to display weak light nonlinearity [S. Gupta \textit{et al}., Phys. Rev. Lett. \textbf{99}, 213601 (2007)]. The model is described by a non-interacting Bose-Einstein condensate contained in a Fabry-P\'{e}rot optical resonator, in which two incommensurate standing-wave modes are excited and thus form a quasiperiodic optical lattice potential for the atoms. Special emphasis are paid to the variation of atomic wavefunction induced by the cavity light field. We show that bistability between the atomic localized and extended states can be generated under appropriate conditions.