Is lasing possible in a 2 level atom if the energy levels are degenerate? When introduced to laser physics we use Einstein Coefficients:

*

*$A_{21}$ = rate of spontaneous emission

*$B_{21}$ = rate of stimulated emission

*$B_{12}$ = rate of stimulated absorption

A standard derivation in a two-level atom in steady state gives $\frac{N_2}{N_1}= \frac{B_{12}\rho}{B_{21}\rho + A_{21}}$   where $\rho$ is the radiation energy density.
If we take the limit $\rho\rightarrow\infty$ we can ignore spontaneous emission and the population of each level becomes approximately the ratio of $B$ coefficients.
Can this ratio not be greater than 1 - particularly if the degeneracy of the energy levels is not equal? And so does this mean population inversion is possible even for 2 energy levels?
 A: Well, its complicated.
In the literal sense, no, its not possible, because we really take the single levels and do not count with splitting of the levels. Any split level will count as its own. Although maybe someone more proficient with laser modeling might say otherwise and give a better answer
But if you consider energy bands, then its similar to what you are getting at.
Take a look at another answer I gave in another question and talk about the specific case of Yb:YAG pumped in the zero-phonon line. question here
In the case of Yb:YAG, you pump from the lowest band of ${}^2F_{7/2}$ which is mainly occupied in its ground state, when at room temperature. You then pump to the lowest level of the ${}^2F_{5/2}$ band and you create an inversion between this level and the degeneracy of the ${}^2F_{7/2}$ band. After stimulated emission (if looking at the image in the other question, from Up1 to Low3) there's thermalization of the electrons within the band (so a redistribution) and the ${}^2F_{7/2}$ stays pretty much occupied only in the ground state.
But as you see, its still a 3-level system, when really looking at which levels are there, but the transitions are only between 2 bands (which are degenerate).
Now if you only consider Low1-Up1, this would be a true 2-level system and in that case, maximum inversion you can achieve is 50%. At that point the material becomes transparent, as for every photon incident on the medium the probability of absorption or emission is the same so there is no net loss or gain.
Hope this helps in any way.
