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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?

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# (im)possibility of a two-level laser

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