Population inversion

The problem: amplifying rather than absorbing

Stimulated emission clones photons — perfect. But there is an obstacle. In an ordinary gas, there are far more atoms in the lower state than in the upper state. A photon is therefore much more likely to be absorbed (by a lower atom) than to trigger a stimulated emission (by an upper atom).

   Situation normale (equilibre) :

   E2 :  o                    (peu d'atomes en haut)
   E1 :  o o o o o o o o      (beaucoup d'atomes en bas)

   -> un photon rencontre surtout des atomes BAS -> il est ABSORBE
   -> pas d'amplification, au contraire : la lumiere s'eteint

For stimulated emission to prevail over absorption, the situation must be reversed: there must be more atoms up top than down below. This is population inversion.

   Inversion de population (etat "anormal") :

   E2 :  o o o o o o o o      (beaucoup d'atomes en HAUT)
   E1 :  o                    (peu en bas)

   -> un photon rencontre surtout des atomes EXCITES
   -> emission stimulee dominante -> AMPLIFICATION

Pumping

This inverted state is not natural (atoms tend to fall back): it must be maintained by force by continually injecting energy to re-excite the atoms. This is pumping — optical (a lamp, another laser) or electrical (a discharge).

   energie de pompage
        |||||||
        vvvvvvv
   [ milieu amplificateur ]  -> maintenu en inversion de population

Why two levels are not enough

An important subtlety: with only two levels, you cannot obtain a lasting inversion. By pumping, you excite atoms toward E2, but the same pumping causes just as many stimulated emissions toward E1: at best, you equalize the two populations, but you never invert them.

The real solution uses three or four levels, with an intermediate metastable level (where atoms stay trapped for a relatively long time before falling back). Atoms accumulate there, which creates the inversion relative to the lower level:

   Systeme a 3 niveaux :

   E3  ----o----         pompage rapide vers E3
             \\ (chute rapide, non radiative)
   E2  --oooooo--  <- niveau METASTABLE : les atomes s'accumulent ici
             |            (inversion E2 > E1 obtenue !)
             | emission stimulee (la transition LASER)
             v
   E1  --o-------  niveau bas

The metastable level acts as a "reservoir": atoms linger there instead of falling back right away, and their number eventually exceeds that of the lower level. The inversion is reached, and amplification becomes possible.

In summary

For stimulated emission to prevail over absorption, there must be more excited atoms than at rest: this is population inversion, an "abnormal" state maintained by pumping (a continuous supply of energy). Two levels are not enough; a three- or four-level system is used, with a metastable state where atoms accumulate, creating the inversion. This is the essential condition for amplifying light.