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We propose and investigate a protocol for Gaussification of quantum states oftraveling light beams in an atomic quantum memory that couples to light viaquantum non-demolition interaction. The protocol relies on a periodic switchingbetween two different QND couplings and the total coupling strength scales onlylogarithmically with number of Gaussified light modes. The present scheme canbe used to prepare entangled states of two distant atomic ensembles and topurify and Gaussify noisy non-Gaussian entangled states of light whilesimultaneously storing the purified state in atomic memories.

Gaussification of quantum states of traveling light beams in atomic memory