How does a laser emit light in a coherent state?

Question

Lasers work by stimulated emission of atomic transitions. Stimulated emission produces two photons which, because the particle number is well-defined, projects the field into a Fock state. However, it is a known fact that lasers emit light in a coherent state. How does the field evolve from a particle-state to a superposition of particle-states? Omitting normalization:

$$ | n \rangle \rightarrow \sum_{n=0}^{\infty}\frac{\alpha^n }{\sqrt{n!}}| n \rangle $$

I guess one way of looking at it is that the field shifts according to $\Delta n \Delta \phi \geq 1$ from certain particle number to certain phase but it feels like a superficial answer to me. What I want to understand is the mechanism that allows this to happen. Is it the reflection with the mirror? Is it the imposed boundaries of the resonating cavity? Pumping method?

Answer 1

You are making an incorrect assumption in your question: There is no physical evolution from a number state (aka Fock state). This evolution happened purely inside physicists' heads as it was realized that laser light is not properly described by number states. The problem is your assumption that the particle number ever is well-defined.

Lasing action is an inherently quantum-mechanical process: A photon interacts with a two-level system in its upper state. Unlike the simplified description you seem to be using, this does not always result in two photons and the two-level system in its lower state. What really happens is that a superposition between that result and the boring one, with no interaction at all, is created. Hence you have a superposition between a light field with one and with two photons. Continue this to the (theoretical, but sensible) limit of infinitely many such interactions (with interaction strength tuned to give your desired mean photon number), and you get coherent states.