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.


Population inversion alone is not the sole requirement for a laser. The reason why we need at least a three-level system is because this inversion needs to provide net gain.

In a two-level system, absorption and emission have the same cross-section, which means that in the general case you maximize your population at 50%. However you talk about a specific special case where an inversion is possible (and that is true). But lets assume that you do use such a process to achieve inversion and that a laser is possible, then you start the laser action and after depletion of that inversion (which can happen really fast), you have a highly absorbing material. You were able to amplify a small signal only up to the point where the inversion was 50%, after that, your medium was solely absorbing. I am not saying it is impossible, but to achieve inversion of enough ions in an adiabatic process to then be able to drive laser action up to the 50% point is too cumbersome, inefficient and does not bring anything good to the table...and maybe to even achieve enough small signal gain with such a system, perhaps the pump would require to be so intense that it would be above the damage threshold of the medium.

The problem is that you need to keep a constant net gain level on the system to make a laser, and the reason why we need at least a three-level system, so that we can keep the medium inverted virtually the whole time. Even in q-switched lasers, as the ground state is cleared quite fast, inversion is easily had throughout the de-excitation and light amplification process (instead of capping at a 50% point).

Hope this helps.

  • $\begingroup$ So if I understood well, in the case that I considered, the problem is not the population inversion (which is possible) but the constant net gain required by the laser. In the two-level system there is a time during which the most of the population is in the lower state, and therefore we cannot have the stimulated emission unless we re-pump the population to the upper state. Did I get the idea somehow? Thanks $\endgroup$
    – quantumik
    Jul 19 at 8:39
  • $\begingroup$ @quantumik yes, it is basically that. $\endgroup$ Jul 19 at 18:53

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.