Coherence Enhanced Transient Lasing in XUV Regime

We report the effect of a coherent drive on transient lasing in three-level $\Lambda $ and $\Xi$ configurations ($c\leftrightarrow a\leftrightarrow b$). We show that the presence of a resonant coherent drive on the $a\leftrightarrow c$ optical transition can yield an order of magnitude enhancement of the output laser energy on a $a\rightarrow b$ XUV or X-ray transition than with no coherent drive. We demonstrate the crucial role of coherence $\varrho_{ac}$ for the laser power enhancement. Contrary to the forward direction (with respect to the pump), where forward gain can be enhanced for some choice of the drive Rabi frequency $\Omega_{c}$, coherent drive on the $ac$ transition always suppresses the backward gain.