Saint-Petersburg State University , Russia

We consider dynamics of a quasi 1D Bose-Einstein condensate (BEC) loaded into an off-resonant leaky cavity or a quantum optical lattice [C.Maschler et al., Eur. Phys. J. D 46, 545 (2008)]. This implies that quantum features of the optical potential are taken into account. Our main concern is the influence of nonlinearity due to atom-atom interactions on the dynamics of BEC. Using positive P representation the evolution of the system is analyzed and numerically solved to demonstrate considerable dependence of the cloud broadening on the atom-atom scattering length. This result is compared with earlier results [T. Yu. Ivanova et al., Phys. Rev. A 84, 043602 (2011)] for harmonically trapped BEC subjected to a generic quantum measurement of its center-of- mass position.