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I'm wondering about achieving population inversion for a laser. I learned that without an active medium, it's not possible to create a laser with only two energy levels, but it would be possible with three. What is the advantage of having four levels then?

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When you have a three-level system, the laser transition is between the ground and first excited levels (see figure). In this scheme, it is rather challenging to get population inversion because all atoms tend to stay on the lowest level.

With a four-level scheme, you have an extra level so that the laser transition does not end in a ground state. Thus, if the bottom level gets depopulated faster than the top level in the laser transition the population inversion will be guaranteed independent of how fast or efficiently you pump the system. Many lasers, such as Nd:YAG or HeNe laser to name a few, actually use a four-level scheme exactly for this reason.

Three- and four-level laser setup.

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I don't understand what happens after the "laser" from E3 -> E2 in the second picture. What happens at the transition from the second level to the ground state? –  Chris Harris Feb 13 '13 at 23:30
    
That is just some non-radiative transition (e.g. through collisions) that, if faster than decay from E$_3$ to E$_2$, guaranties that the population inversion will be achieved. –  Ondřej Černotík Feb 14 '13 at 8:14

If you have a fast non-radiative transition to the ground state from the bottom laser level, that would help with population inversion because you're emptying the bottom laser level.

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What you mentioned is correct for three-level scheme. What is the advantage of fourth level? –  Misha Feb 14 '13 at 10:29

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