  In this work, we use the quantum-jump approach to study light-matter
interactions in a four-level scheme giving rise to frequency up-conversion
amplification without inversion (AWI). The results obtained apply to the case
of neutral Hg vapour where, recently, it has been reported AWI of a probe field
in the UV regime, opening the way for lasing without inversion in this range of
frequencies. We show that, in this scheme, the key element to obtain maximum
amplification is the fulfillment of the three-photon resonance condition, which
favors coherent evolution periods associated with the probe field gain. We also
investigate the parameter values in order to optimize amplification. The
present study extends the theoretical understanding of the underlying
mechanisms involved in AWI.
