I am reading a text on coherent radiation and not quite understanding a particular statement. To provide some background, the authors state that coherent radiation can arise from light-matter interactions even when considering lengths, $L$, much smaller than the wavelength (i.e. $V \sim L^3 \ll \lambda^3$) due to phase coherence in the medium if it satisfies certain conditions (e.g. initial population inversion, dephasing effects are negligible on the time-scale, $T_P$, of the coherent bursts of radiation). Now the author states the following about the regime where $T_P < \lambda / c$ :

"This regime is not physical: in order to observe it, one would have to realize the inversion of the medium in a time shorter than the optical period."

It may be quite obvious what the author is saying, but why exactly cannot the burst occur on a timescale quicker than the optical period? If an ensemble of atoms, with $L < \lambda$ can coherently radiate, why can't atoms radiate on timescales of less than $\lambda / c$? As long as they are sufficiently close and the interactions causal (i.e. $T_P > \Delta x / c$), why can't coherent radiation occur? Perhaps at such high densities, dipole-dipole interactions may disrupt the process, but I don't quite understand the significance of $T_P$ needing to be larger than the optical period. Any thoughts?



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