(im)possibility of a two-level laser

[Ameno]

Hi

I would like to understand the statement that "there cannot be a two-level laser" in a bit more detail.
I understand that given an active medium consisting of two-level systems, one cannot pump it using photons with an energy equal to the energy gap to reach population inversion, because in the stationary state, the rates of absorption and emission are equal (which means that we cannot have pumping and population inversion at the same time). Therefore, there cannot be a two-level laser pumped by photons.

But what about two-level lasers that are pumped in a different way? For instance, isn't a laser diode a two-level laser? I don't see an argument that prevents two-level systems from being pumped by something else than photons (e.g. inelastic collision). Are there such lasers? How far is the statement "there cannot be a two-level laser" still valid?

 

[gujax]

Hi

But what about two-level lasers that are pumped in a different way? For instance, isn't a laser diode a two-level laser? I don't see an argument that prevents two-level systems from being pumped by something else than photons (e.g. inelastic collision). Are there such lasers? How far is the statement "there cannot be a two-level laser" still valid?

Hmm, interesting! Are you talking about non-optically pumped diode lasers in which an external current induces lasing?
But then you are now no more really talking about a closed system. The above statement is strictly true for a radiative closed system. If you bring in particles from outside you are no more talking about two-level systems.

Now if you use inelastic collisions to pump the electrons to upper levels, my guess is the inelastic collisions will work both ways i.e., even excited state particles can collide with the low energy particles which have just lost their energy by collisions and the two rates may equilibrate. Why should reverse process be restricted i.e., process A to B should be same as rate of process B to A. But you are correct that if such a collision process exists, then surely you would have a laser.
For example A to B process could be a chemical reaction in which A to B is an excitation process and the equilibriation rates can be such that B > A.
I wonder if you have looked at chemical lasers? I do not have much idea about those. It maybe possible that they do break the two level rule you talk about.

 

[DrDu]

I think most masers like the ammonia maser work with only two levels. The molecules being in the ground state are simply filtered out with a magnetic lens before entering the resonator. I don't see why this shouldn't work in the optical region as well.

 

[Ameno]

Sorry for the late answer, and thank you for your replies which confirm my guess that things are somewhat more subtle than claimed by the above statement. For example, I asked a Ph.D. student who is engaged in quantum electronics about the diode laser that I proposed as a counterexample, and he agreed that people often regard a diode laser as a two-level laser, although there are rather energy bands than energy levels, so in this case the question about the existence of a two-level laser is rather a question about the acceptance of the notion.
After all, one should say "there is no optically pumped two-level laser".