One- and two-photon absorption-amplification response in a four-level atomic system with vacuum-induced coherence

This paper theoretically studies the effects of the vacuum-induced coherence on one- and two-photon absorption in a four-level atomic medium. It finds that the one- and two-photon absorption and amplification properties are quite sensitive to the vacuum-induced coherence. It is also shown that the one- and two-photon absorption spectra can be dramatically affected by modulating the relative phase of the applied fields. With the proper choice of the relative phase, the amplification without inversion for the probe field can be realized.