Atomic state that is a coherent superposition?

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meyol99
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Can someone explain the meaning of the k vector and the general meaning of this equation?
 

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Nicolas Sangouard, Christoph Simon, Hugues de Riedmatten, and Nicolas Gisin
"Quantum repeaters based on atomic ensembles and linear optics",
Rev. Mod. Phys. 83, 33 – Published 21 March 2011