Why Are All Photons in a Laser Beam Coherent?

[huyen_vyvy]

just wondering why all photons produced in a laser beam are coherent? what forces them to have the same phase?

 

[cesiumfrog]

and does it violate the no-cloning theorem?

 

[dimali]

what makes them coherent is an instability that they all go through at the same time. So by moving the end mirror suddenly, there is an instability and when they start to propagate again, they are moving in phase.

 

[alxm]

just wondering why all photons produced in a laser beam are coherent? what forces them to have the same phase?

They have the same phase because the vast majority of photons are emitted through the process known as stimulated emission (laSEr). One photon "stimulates" a decay from one electronic energy level to another (if the energy is the same), so you get two photons of the same frequency, and they're always in phase. (as opposed to spontaneous emissions which have random phase)

You probably know this, since your question is: Why are they in phase? The short, abridged version is that the process is akin to resonance. The oscillating electric field of the stimulating photon is what stimulates the emission, and it's sort-of intuitive that the emitted photon would 'resonate' with it, in other words, be in phase.

(not that you should really accept 'intuitive' explanations, but it'd take some time-dependent perturbation theory to explain it properly)

 

[Manchot]

Fundamentally, it's because of quantum mechanics. When you quantize the electromagnetic modes of a system, you find that each modes' quadratures—the mode's amplitude and its time-derivative—have a Hamiltonian identical to the mechanical harmonic oscillator, only amplitude has replaced position and amplitude's time-derivative has replaced momentum. Quantum mechanics then tells you that the energy eigenstates of the mode can only occur in discrete steps of $\hbar \omega$.

The rest is really semantics. If an electron could add energy to the mode by adding an a photon of arbitrary phase to the mode's amplitude, it would change the energy by an amount other than $\hbar \omega$. However, this is quantum mechanically forbidden, so its only possibilities are to do nothing, to absorb $\hbar \omega$ from the field by adding a field completely out-of-phase, or to emit $\hbar \omega$ into the field by adding a field completely in-phase.