We develop the analytical theory that describes simultaneous transmission of several photons through a waveguide coupled to a Λ-type atom. We show that after transmission of a short few-photon pulse, the final state of the atom and all the photons is a genuine multipartite entangled state belonging to the W class. The parameters of the input pulse are optimized to maximize the efficiency of three- and four-partite W-state production. The probability to obtain the canonical W state of many photons is shown to be larger than 1/e.
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Ilin et al. (2024) studied this question.
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