Effects of temperature and ground-state coherence decay on enhancement and amplification in a $\mathrm{\Delta }$ atomic system

We study phase-sensitive amplification of electromagnetically induced transparency in a warm ${}^{85}$Rb vapor wherein a microwave driving field couples the two lower-energy states of a {\Lambda} energy-level system thereby transforming into a {\Delta} system. Our theoretical description includes effects of ground-state coherence decay and temperature effects. In particular, we demonstrate that driving-field-enhanced electromagnetically induced transparency is robust against significant loss of coherence between ground states. We also show that for specific field intensities, a threshold rate of ground-state coherence decay exists at every temperature. This threshold separates the probe-transmittance behavior into two regimes: probe amplification vs probe attenuation. Thus, electromagnetically induced transparency plus amplification is possible at any temperature in a {\Delta} system.