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Quantum theory of coupled three- frequency optical parametric interactions, multipartite entangled states

A. S. Chirkin, Alexander Mikhailovich Chebotarev, Timur Tlyachev

Published Jan 1, 2013• 0 citations
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We describe the normal ordering method (NOM) as a convinient way to obtaining explicit forms of the state vectors and density matrices of quantum states, usually generated in multiple coupled parametric optical processes. As a specific example, our method is demonstrated for the states, generated in three second-order parametric optical processes - one parametric down-conversion accompanied by two up-conversion processes. The application of the method allowed us to calculate the entropic characteristics of the multipartite quantum system.
A general approach is considered to find wave function and density operator evolution of the systems including the arbitrary number of coupled optical parametric interactions described by the quadratic Hamiltonian. This approach is based on the time-dependent canonical transformations that define the evolution of the system in the Heisenberg picture or in the interaction picture. An application is illustrated with four-frequency entangled light fields, which can be produced at the nonlinear optical interactions in vapors and solid states. The process includes one non-degenerate parametric down-conversion followed by two parametric up-conversions occurring in the field of the same classical pumping wave.