  All experiments with ultracold atoms are performed in the presence of
background residual gas. With the help of a suitable master equation we
investigate a role of these fast atoms on the loss of coherence in optical
lattices. We present an exact solution of the master equation and give the
analytic formulas for all correlation functions in the presence of one body
losses. Additionally we discuss existing of a Schr\"odinger cat state predicted
in this system in [1].
