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When energy is pumped into the atom, photon is being emitted which would then get absorbed by another already excited atom causing the atom to emits 2 similar photon. Soon more photons are produced in this manner which escapes through a hole as seen as laser light, my question is are all these photons entangled?

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In an ideal laser, there is no entanglement whatsoever between successive emerging photons. This occurs because a laser state is supposed to be a coherent state (Glauber state) of the electromagnetic field. One of the properties of such a state is that removing one quantum of energy from it does not actually change the state of the system. (The coherent states are eigenstates of the annihilation operator.) So, essentially, when a photon is released from the laser cavity, the state of the cavity does not change. (This is consistent with energy conservation because there is a continuous pumping of energy into the cavity.)

As a consequence of this lack of entanglement, the laser photons are emitted in a Poisson process. That means the emission time of any one photon is uncorrelated with the emission times of all the others. There are no higher order correlations either. (This can be described by saying that the laser is perfectly coherent at all orders.)

Real lasers deviate somewhat from this ideal somewhat, for various reasons, some obvious, some not. (A laser that is only turned on for a finite time cannot be perfectly coherent. There are also more complicated imperfections that can arise from the way the system is pumped if more than two states are involved.) However, in general, the goal of a laser system is to produce a beam that is as close to a perfectly coherent structure as possible.

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  • $\begingroup$ Does the 2nd photon which was stimulated have any correlation in time to the original photon? Simultaneous? $\endgroup$ – PhysicsDave Dec 12 '18 at 3:08
  • $\begingroup$ @PhysicsDave Photons in a laser do not come in pairs. As I said, "the emission time of any one photon is uncorrelated with the emission times of all the others." $\endgroup$ – Buzz Dec 12 '18 at 3:13
  • $\begingroup$ So it's interesting that the stimulated emission comes in a Poisson distribution but that in the laser many of the photons have similar phase ...I'm not an expert just trying to understand it. $\endgroup$ – PhysicsDave Dec 12 '18 at 3:21
  • $\begingroup$ @PhysicsDave “Laser radiation is produced in a resonant cavity where the resonant frequency of the cavity is the same as the frequency associated with the atomic electron transitions providing energy flow into the field. As energy in the resonant mode builds up, the probability for stimulated emission, in that mode only, increases. That is a positive feedback loop in which the amplitude in the resonant mode increases exponentially until some non-linear effects limit it. ” $\endgroup$ – HolgerFiedler Dec 12 '18 at 5:36
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    $\begingroup$ I think you should hold your horses a bit, lasing is a quantum mechanical phenomenon and if a single wave function can be obtained for the system there may be entanglement see agencia.fapesp.br/… . Also physicsworld.com/a/laser-beams-are-entangled-in-space . Also I would not confuse coherence, which means fixed phases in the wavefunctions, with non entanglement. $\endgroup$ – anna v Dec 12 '18 at 12:06

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