Coherent Photons: Uncertainty and Locality

[Marrrrrrr]

I understand that laser is based on the phenomenon of coherence. But I wonder how, say, two photons could be said to be located at the exact same spot when their locations could not be precisely defined due to the principle of uncertainty.

To specify, which between the following two would be closer to the truth?

(1) They are "roughly" located at the same spot, which is enough for practical purposes.

(2) They are quite literally at the exact same spot, although it is not well-defined precisely at which spot they are colocated.

 

[PeterDonis]

I wonder how, say, two photons could be said to be located at the exact same spot

They can't. But that's not what "coherence" means. It means, heuristically, that you have many photons in the same quantum state, not many photons at the same position.

 

[Marrrrrrr]

They can't. But that's not what "coherence" means. It means, heuristically, that you have many photons in the same quantum state, not many photons at the same position.

Okay, thanks. But isn't it that one of those quantum states they share is about their positions?

 

[PeterDonis]

isn't it that one of those quantum states they share is about their positions?

There is only one quantum state involved. Strictly speaking, it's not a state that is "shared" by all the photons: it's a single quantum state of the many-photon system. (Really strictly speaking, this state does not even have a definite photon number, but that's probably going deeper than we need to here.)

As for position, there is no well-defined position operator for photons (or for any massless particles), so no, the quantum state in question is not about positions in any useful sense.

 

[DrChinese]

I understand that laser is based on the phenomenon of coherence. But I wonder how, say, two photons could be said to be located at the exact same spot when their locations could not be precisely defined due to the principle of uncertainty. ...

Presumably you know that the photons in a laser are said to be in phase, and will have the same polarization.