Phase-dependence of inversionless gain in a Doppler broadened open four-level system

Abstract The effect of the relative phase ( ϕ ) between the probe and driving fields on the gain without inversion (GWI) in a Doppler broadened open quasi Λ-type four level atomic system with vacuum induced coherence (VIC) for both co- and counter-propagating probe and driving fields cases is studied. It is shown that: (1) GWI and the probe detuning region in which GWI exists are very sensitive to variation of the relative phase; when values of the other parameters keep unvarying, by adjusting value of ϕ , the largest GWI can be obtained. (2) The Doppler width ( D ) also has dramatically modulation role on the phase-dependent GWI. When value of D is smaller, the value of ϕ which corresponds to the largest value of GWI is about π , when value of D is large enough, it is about π /2. (3) GWI varies periodically with ϕ varying, the period is 2 π , but the concrete variation rule is closely related to value of D . (4) In the co-propagating case we can obtain much larger GWI than that in the counter-propagating case.