Propagation of quantum field interacting with single two-level or three-level atoms has been studied. Using the Gaussian quantum mode functions, we calculate evolution of the quantum state that includes atomic and field variable. We demonstrated the phase acquired by the single photon propagation that can be of great importance for long quantum communications. The results can be used for controlling quantum field propagation, and for design of optical elements such as a quantum prism and a quantum lens. The vacuum fields have been used to generate the strongly correlated quantum fields.
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Yuri V. Rostovtsev (2024) studied this question.
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