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If laser light is described by a coherent state, a macroscopic quantum state, to what extent does it make sense to speak of individual photons in laser light?

And if the laser is attenuated to be a single photon source, is it still valid to describe the laser light by a coherent state?

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  • $\begingroup$ see this one photon at a time double slit experiment, a laser is used : sps.ch/artikel/progresses/… $\endgroup$ – anna v Jun 9 at 14:31
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    $\begingroup$ An attenuated laser is not a single photon source! $\endgroup$ – Norbert Schuch Jun 9 at 17:17
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The second question is easiest to answer: yes! An attenuated laser still takes the form $$|\alpha\rangle=e^{-|\alpha|^2/2}\sum_{n=0}^\infty \frac{\alpha^n}{\sqrt{n!}}|n\rangle,$$ just with sufficiently small $|\alpha|$ such that the average number of photons $\bar{n}=e^{-|\alpha|^2}\sum_{n=0}^\infty n\frac{|\alpha|^2}{n!}$ is small (can be much smaller than 1 on average, if you like).

For the first question, the answer is somewhat. The Poissonian number statistics of a coherent state imply that each photon is in some sense uncorrelated from the other photons. Thus, the probability of detecting $N$ photons can be computed by treating each photon's detection probability independently. In circumstances such as phase estimation this means that each photon can in some sense be treated independently.

On the other hand, there are circumstances in which the photons in a laser should be treated as a collective entity. For example, a laser beam interacting with a two-level atom in the Jaynes-Cummings model has the dynamics split into subspaces that only couple neighbouring photon-number states $|n\rangle$ and $|n+1\rangle$, in which the probability of the atom being in the ground or excited state oscillates with a frequency that depends on $n$. These dynamics cannot be explained by considering lasers to simply be collections of individual photons.

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Both a strong laser and an attenuated one can be described by a coherent state. For the attenuated laser an $|\alpha|\approx 1$ is used to describe it. As with any coherent state the distribution of photons is given by the Poisson distribution. Therefore, there is a randomness on the amount of photons arriving at the detector per unit time as shown:

enter image description here Sometimes 1 photon, sometimes 0 photons, fewer times 2 and so on.

This is different from a "single photon source" which is a quantum state of light such as a Fock state $\left|n\right\rangle$ for which always $n$ photons arrive per per unit time.

For both the strong and weak laser the photon description makes sense, as in it gives the right answer. However, in most cases with strong lasers, the complication of the quantum description is not worth it for the increase in precision gained.

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No, because a one-photon source does not necessary needs a stimulated radiation, to say the least. (A one-photon source is not a laser.)

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