In the book Quantum Optics by Scully and Zubairy it is mentioned that the finite linewidth of the laser is essentially due to spontaneous emission events that randomize the phase. My question is; why does spontaneous emission randomize the phase, but stimulated emission doesn't? Their model uses a single cavity mode coupled to a thermal bath at zero temperature.
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Even if all atoms spontaneously emitted at the same time, the radiation would have non-zero spectral width, because the radiation will be very intense only for a short time (in case of hydrogen atom, nanoseconds). Only infinitely running sine wave would have zero-width emission spectral line, most intensity of real emissions is emitted during a finite time and thus these emissions always have non-zero spectral width. – Ján Lalinský Jan 09 '24 at 23:46
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The spontaneous emission events occur randomly in time, so phase is equally distributed over the unit circle.
Stimulated emission is induced as a jump between two electron states by the dipole field of the external em field. The electron jump simply acts as a creation operator in the incoming mode, adding one energy quantum of the same $(\omega, k)$ in phase.
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Their model uses a single mode cavity, so $\omega$ and $k$ should be the same. I assume this would take away this randomness. Also since, their external reservoir is at zero temperature, it should not lead to fluctuations inside the cavity right? – Chan Jan 09 '24 at 18:11