I was studying the classic two-level system where population inversion can be realized through a $\pi$-pulse or Rapid Adiabatic Passage, like the landau-zener case. The professor said that such an Hamiltonian can be exactly realized experimentally. Then, I also know that, for realizing a laser, we need three levels in order to perform a population inversion, and cannot be done with only two levels. So my question is: if we can realize the population inversion in a two-level system with a simple $\pi$-pulse, why we need three levels for the laser? Maybe the word "population" has a different meaning in the two cases?
I know that with two levels we cannot realize a laser because we reach the limit when the stimulated emission is equally likely with the absorption, but then why the theory says we can do population inversion?
Sorry, I am little bit confused about that.