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As well known in the theory of quantum optics, the photon coherent state is defined by $$\hat{a}|\alpha\rangle = \alpha|\alpha\rangle$$ where $\hat{a}$ is the annihilation operator. Explicitly this state can be written as $$|\alpha\rangle = e^{-\frac{|\alpha|^2}{2}} \sum_{n = 0}^{\infty}{\frac{\alpha^n}{\sqrt{n!}}|n\rangle}$$ where $|n\rangle$ is the photon number state in the Fock space. $\alpha$ is a complex parameter, namely, $\alpha=|\alpha|e^{i\phi}$.

Where can I find any papers or references that have described the detail of the experiment for realizing the above photon coherent state?

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  • $\begingroup$ I am not sure if single photon coherence is the same as general coherence. It usually is just a matter of spatial filtering (one single $k$ vector) and temporal filtering (one single frequency $\omega$) and then your phase is well behaved and the electromagnetic field has coherence properties. The wikipedia article on coherence explains this $\endgroup$ Commented Jun 15, 2020 at 9:29
  • $\begingroup$ The wiki article contains several references. $\endgroup$
    – NotMe
    Commented Jun 15, 2020 at 17:47

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