Gain enhancing due to quantum interference effect in an open four-level atomic system with Doppler broadening

The effect of vacuum-induced coherence (VIC) on the gain of lasing without inversion (LWI) is studied in an open four-level atomic system with Doppler broadening for both cases: co- and counter-propagating probe and driving fields. The results show that: (1) in general, for a fixed VIC strength, LWI gain decreases monotonously with the value of the Doppler broadening width increasing. Regardless of the Doppler broadening being obvious or not, the LWI gain much larger than that without VIC always can be gotten by choosing suitable VIC strength, i.e. values of two factors p1 and p2 which represent the VIC effect. (2) Varying p1 or p2 will produce remarkable different influence on the LWI gain, and the influence is closely related to the value of the Doppler broadening width. (3) In the case of counter-propagating probe and driving fields, when the Doppler broadening is large enough, gain oscillation occurs. For the same value of the Doppler broadening width, the oscillation amplitude increases with increasing values of strength of VIC. (4) The atomic exit and injection rates also can dramatically affect LWI gain. (5) The LWI gain for the co-propagating probe and driving fields is always larger than that for the counter-propagating probe and driving fields. (6) A much larger LWI gain in open system than that in the corresponding closed system can be obtained.