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The radiation emitted by a classically pumped three-level $\Lambda$-typeemitter in a resonator cavity featuring both radiative and unwanted losses isstudied. In particular, the efficiency of one-photon Fock state excitation ofthe outgoing wave packet and the spatio-temporal shape of the wave packet areinvestigated. It is shown that for given shape of the emitter--cavityinteraction, adjusting the shape of the pump pulse renders it possible togenerate the emission of one-photon Fock state wave packets of desired shapewith high efficiency.

Cavity-assisted spontaneous emission of a single $\Lambda$-type emitter as a source of single-photon packets with controlled shape