Mapping generalized Jaynes-Cummings interaction into correlated finite-sized systems

Abstract: We consider a generalized Jaynes-Cummings model of a two-level atom interacting with a multimode nondegenerate coherent field. The sum of the mode frequencies is equal to the two-level transition frequency, creating the resonance condition. The intermediate levels associated with the multi-photon process are adiabatically eliminated using the non-resonant conditions for these transitions. Under such general conditions, the infinite atom-multiphoton interaction is effectively mapped onto an equivalent reduced \textit{2}$\times$\textit{2} bipartite qubit system that facilitates the study of the nonclassical features of the interaction using known information-theoretic measures. We observe that the bipartite pure system is highly entangled as quantified by its entanglement of formation. Further, it is shown that the dynamics of the mapped system can be generated using optically truncated, quantum scissored states that reduce the infinite atom-multiphoton interaction to a finite \textit{2}$\times$\textit{k} system, where $k$ is a suitable truncation number. This allows us to introduce atomic dephasing and study the mixed state dynamics, characterized by the decay of quantum correlations such as quantum discord, which is observed to be more robust than entanglement. The quantum correlation dynamics of the dissipative system qualitatively complements the behavior of collapse and revival of the Rabi oscillations in the system. The effective mapping of the composite system proves to be an efficient tool for measuring information-theoretic properties.