  We propose and investigate a protocol for Gaussification of quantum states of
traveling light beams in an atomic quantum memory that couples to light via
quantum non-demolition interaction. The protocol relies on a periodic switching
between two different QND couplings and the total coupling strength scales only
logarithmically with number of Gaussified light modes. The present scheme can
be used to prepare entangled states of two distant atomic ensembles and to
purify and Gaussify noisy non-Gaussian entangled states of light while
simultaneously storing the purified state in atomic memories.
