**Matter copy dynamics in a BEC**

Light can be stored in Bose-Einstein condensates for more than one second using quantum memory techniques based on electromagnetically induced transparency [1]. In recent theoretical work [2], Rispe et al. proposed a method for storing photons in Bose-Einstein condensates to create a photon-photon gate. This gate uses the collisions between atoms in order to generate a phase shift that is dependent on the presence or absence of photons. We go beyond the single photon case considered in the previous scheme [2] to the many-photon case in the mean-field treatment and under the Thomas-Fermi approximation, where this scheme leads to strong phase self-modulation. That medium will allow superposition of an arbitrary number of photons to undergoing nonlinear evolution and in particular produce "cat states" [3]. We generate "cat states" [3] from coherent states through the collision-induced interaction.
References: [1] R. Zhang, S. R. Garner, and L.V. Hau, Phys. Rev. Lett. 103, 233602 (2009). [2] A. Rispe, B. He, and C. Simon ,Phys. Rev. Lett. 107, 043601 (2011). [3] B. Yurke, and D. Stoler, Phys. Rev. Lett. 57, 13 (1986).