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This is a follow-up to this recent answer by Wouter to this related question from 2015, and a comment by Emilio Pisanty underneath.

I have read the papers by Mølmer, Bartlett et al., Wiseman, and parts of van Enk and Fuchs referenced therein. I have a clear idea of the justification (even derivation) of the mixed state $$\frac1{2π} \int |α e^{iφ}\rangle \langle α e^{iφ}| \mathrm{d}φ = e^{-μ} \sum_n \frac{μ^n}{n!} |n\rangle \langle n|.$$ But I want to agree with Bartlett et al.'s "factist" and see the emergence of the pure state $$|\sqrtμ\rangle = e^{-μ/2} \sum_n \sqrt{\frac{μ^n}{n!}} |n\rangle.$$

Here's what Wiseman has to say about it:

Thus, the phase reference laser beam in the teleportation experiment is in a coherent state. It is not a coherent state of unknown phase; it is the coherent state $|μ\rangle$, with zero phase (relative to itself).

and

In particular, if the laser itself is the clock then by definition it is coherent with respect to itself so it should be described by a pure state $|μ\rangle$ of zero phase.

I don't understand these claims. What does the author mean by "then by definition it is coherent with respect to itself"? Surely within coherence theory (the $g^{(n)}$ functions) an ideal laser is coherent to all degrees but I am quite sure that is a property of the Poissonian mixture as well, which would not prioritize the pure state in any way.

Furthermore, the arguments of virtually everyone are refuted in the Bartlett et al. paper, including Wiseman's quote above and van Eck and Fuchs' reference to the de Finetti theorem, but I can not infer any mathematicsthe particular form of the pure state from allany part of the talk about the reference frames, only reasoningthat the two lead to the same measurable results. (I am very sure I am just lacking some context there.) I don't need to show that the coherent state works, or that it is not necessary for explaining the experiments. I want to derive it.

My question is simple: how, of all possible states which share the same photon statistics and coherence degrees, do I extract exactly the formula for the coherent state?

The discussion has grown just far too long and deep to follow in the original literature, so I'm asking for a quick summary from someone who's already familiar with it.

This is a follow-up to this recent answer by Wouter to this related question from 2015, and a comment by Emilio Pisanty underneath.

I have read the papers by Mølmer, Bartlett et al., Wiseman, and parts of van Enk and Fuchs referenced therein. I have a clear idea of the justification (even derivation) of the mixed state $$\frac1{2π} \int |α e^{iφ}\rangle \langle α e^{iφ}| \mathrm{d}φ = e^{-μ} \sum_n \frac{μ^n}{n!} |n\rangle \langle n|.$$ But I want to agree with Bartlett et al.'s "factist" and see the emergence of the pure state $$|\sqrtμ\rangle = e^{-μ/2} \sum_n \sqrt{\frac{μ^n}{n!}} |n\rangle.$$

Here's what Wiseman has to say about it:

Thus, the phase reference laser beam in the teleportation experiment is in a coherent state. It is not a coherent state of unknown phase; it is the coherent state $|μ\rangle$, with zero phase (relative to itself).

and

In particular, if the laser itself is the clock then by definition it is coherent with respect to itself so it should be described by a pure state $|μ\rangle$ of zero phase.

I don't understand these claims. What does the author mean by "then by definition it is coherent with respect to itself"? Surely within coherence theory (the $g^{(n)}$ functions) an ideal laser is coherent to all degrees but I am quite sure that is a property of the Poissonian mixture as well, which would not prioritize the pure state in any way.

Furthermore, the arguments of virtually everyone are refuted in the Bartlett et al. paper, including Wiseman's quote above and van Eck and Fuchs' reference to the de Finetti theorem, but I can not infer any mathematics from all the talk about reference frames, only reasoning. (I am very sure I am just lacking some context there.)

My question is simple: how, of all possible states which share the same photon statistics and coherence degrees, do I extract exactly the formula for the coherent state?

The discussion has grown just far too long and deep to follow in the original literature, so I'm asking for a quick summary from someone who's already familiar with it.

This is a follow-up to this recent answer by Wouter to this related question from 2015, and a comment by Emilio Pisanty underneath.

I have read the papers by Mølmer, Bartlett et al., Wiseman, and parts of van Enk and Fuchs referenced therein. I have a clear idea of the justification (even derivation) of the mixed state $$\frac1{2π} \int |α e^{iφ}\rangle \langle α e^{iφ}| \mathrm{d}φ = e^{-μ} \sum_n \frac{μ^n}{n!} |n\rangle \langle n|.$$ But I want to agree with Bartlett et al.'s "factist" and see the emergence of the pure state $$|\sqrtμ\rangle = e^{-μ/2} \sum_n \sqrt{\frac{μ^n}{n!}} |n\rangle.$$

Here's what Wiseman has to say about it:

Thus, the phase reference laser beam in the teleportation experiment is in a coherent state. It is not a coherent state of unknown phase; it is the coherent state $|μ\rangle$, with zero phase (relative to itself).

and

In particular, if the laser itself is the clock then by definition it is coherent with respect to itself so it should be described by a pure state $|μ\rangle$ of zero phase.

I don't understand these claims. What does the author mean by "then by definition it is coherent with respect to itself"? Surely within coherence theory (the $g^{(n)}$ functions) an ideal laser is coherent to all degrees but I am quite sure that is a property of the Poissonian mixture as well, which would not prioritize the pure state in any way.

Furthermore, the arguments of virtually everyone are refuted in the Bartlett et al. paper, including Wiseman's quote above and van Eck and Fuchs' reference to the de Finetti theorem, but I can not infer the particular form of the pure state from any part of the talk about the reference frames, only that the two lead to the same measurable results. (I am very sure I am just lacking some context there.) I don't need to show that the coherent state works, or that it is not necessary for explaining the experiments. I want to derive it.

My question is simple: how, of all possible states which share the same photon statistics and coherence degrees, do I extract exactly the formula for the coherent state?

The discussion has grown just far too long and deep to follow in the original literature, so I'm asking for a quick summary from someone who's already familiar with it.

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The Vee
The Vee
  • 1.3k
  • 7
  • 18

Why is laser light described by a coherent state?

This is a follow-up to this recent answer by Wouter to this related question from 2015, and a comment by Emilio Pisanty underneath.

I have read the papers by Mølmer, Bartlett et al., Wiseman, and parts of van Enk and Fuchs referenced therein. I have a clear idea of the justification (even derivation) of the mixed state $$\frac1{2π} \int |α e^{iφ}\rangle \langle α e^{iφ}| \mathrm{d}φ = e^{-μ} \sum_n \frac{μ^n}{n!} |n\rangle \langle n|.$$ But I want to agree with Bartlett et al.'s "factist" and see the emergence of the pure state $$|\sqrtμ\rangle = e^{-μ/2} \sum_n \sqrt{\frac{μ^n}{n!}} |n\rangle.$$

Here's what Wiseman has to say about it:

Thus, the phase reference laser beam in the teleportation experiment is in a coherent state. It is not a coherent state of unknown phase; it is the coherent state $|μ\rangle$, with zero phase (relative to itself).

and

In particular, if the laser itself is the clock then by definition it is coherent with respect to itself so it should be described by a pure state $|μ\rangle$ of zero phase.

I don't understand these claims. What does the author mean by "then by definition it is coherent with respect to itself"? Surely within coherence theory (the $g^{(n)}$ functions) an ideal laser is coherent to all degrees but I am quite sure that is a property of the Poissonian mixture as well, which would not prioritize the pure state in any way.

Furthermore, the arguments of virtually everyone are refuted in the Bartlett et al. paper, including Wiseman's quote above and van Eck and Fuchs' reference to the de Finetti theorem, but I can not infer any mathematics from all the talk about reference frames, only reasoning. (I am very sure I am just lacking some context there.)

My question is simple: how, of all possible states which share the same photon statistics and coherence degrees, do I extract exactly the formula for the coherent state?

The discussion has grown just far too long and deep to follow in the original literature, so I'm asking for a quick summary from someone who's already familiar with it.