Coherent and Incoherent States of the Radiation Field. R. J. Glauber in Phys. Rev. 131:2766 (1963).  What the paper says!?

This is an extended version of Glauber's Phys. Rev. Lett. on the topic:

much of the present paper [is] to explaining the background of the material reported [in Ref. ].

And the text where he more clearly discusses the controversy with Sudarshan.

As always from Glauber, it's replete with interesting comments, e.g., on how optics was let behind by quantum field theory:

very little of the insight of quantum has been brought to bear on the electrodynamics problems of optics.

On QED vs multiphotonics (quantum optics):

Most of the mathematical development of quantum electrodynamics to date has been carried out through the use of a particular set of quantum states for the 6.eld. These are the stationary states of the noninteracting field, which corresponds to the presence of a precisely dered number of photons. The need to use these states has seemed almost axiomatic inasmuch as nearly all quantum electrodynamical calculations have been carried out by means of perturbation theory. It is characteristic of electrodynamical perturbation theory that in each successive order of approximation it describes processes which either increase or decrease the number of photons present by one. Calculations performed by such methods have only rarely been able to deal with more than a few photons at a time.

He cites Schwinger for using coherent states «as generating functions for the n-quantum states.»

This is where he most didactically introduces the coherent state

also described in terms of the displacement operator, which, furthermore, is nicely related to the creation-operator picture (Eqs. (3.21‒3.24)).

Section IV «EXPANSION OF ARBITRARY STATES IN TERMS OF COHERENT STATES» is an interesting discussion on mathematical properties of analytic functions derived from the Fock decomposition.

Describing the $P$ expansion:

Such expansions have the property that whenever the field possesses a classical limit, they render that limit evident while at the same time preserving an intrinsically quantum-mechanical description of the field.

Or in more details:

brings to light many similarities between quantum electrodynamical calculations and the corresponding classical ones. Its use offers deep insights into the reasons why some of the fundamental laws of optics, such as those for superposition of fields and calculation of the resulting intensities, are the same as in classical theory, even when very few quanta are involved.

In particular, he argues following Eqs. (7.22-7.23) on the classical laws of interferences:

When two fields described by distributions P& and P2 are superposed, the resulting intensities are found from rules of the form which have always been used in classical electromagnetic theory. For unphased fields the intensities add "incoherently"; for coherent states the amplitudes add "coherently. "

It would be interesting to cast this interpretation in terms of our $g^{(2)}$ interferences (with the $\mathcal{I}_k$ coefficients).

When introducing first the $P$ representation, he cites Sudarshan, first in a footnote:

At this occasion, he makes these important comments (for historical purposes):

where he states that «in general, it is not possible to interpret the function P(α) as a probability distribution in any precise way since the projection operators ». He also cites negativity (and relates it to the Wigner distribution) as further evidence «to underscore the fact that the weight function P(α) cannot, in general, be interpreted as a probability density.»

Later on, again:

While these similarities make applications of the correspondence principle particularly clear, they must not be interpreted as indicating that classical theory is any sort of adequate substitute for the quantum theory. The weight functions P(n) which occur in quantum theoretical applications are not accurately interpretable as probability distributions, nor are they derivable as a rule from classical treatments of the radiation sources. They depend upon Planck's constant, in general, in ways that are unfathomable by classical or semiclassical analysis.

In his additional comments «to discuss the relation between the P representation and the classical theory a bit further», he comes to the conclusion that the $P$ function has a suitable classical interpretation in the limit of large intensities.

Again when coming to the thermal state:

However, because the coherent states $\ket{\alpha}$ are not an orthogonal set, P(α) can only be accurately interpreted as a probability distribution for (n)>>1.

This is also, by the way, where the thermal state seems to be first introduced in quantum optics (modulo its relation to black-body Bose-Einstein distribution):

An even more compelling point on the limitations of the $P$ function as a classical object is made with the ultraviolet catastrophe, and is worth closer attention.

On classical sources generating coherent states:

The radiation by any prescribed current distribution, in other words, always leads to a pure coherent state.

Interesting observation that "well-behaved" fields (with $P$ function having no higher singularities than $\delta$ functions) feature superpositions with an infinite number of photons:

There is thus no upper bound to the number of photons present when the function P is well behaved

It is also where he derives superpositions of fields as convolutions of $P$ functions: «The simple convolution law for combining the weight functions is one of the unique features of the description of fields by means of the P representation. It is quite analogous to the law we would use in classical theory to describe the proba- bility distribution of the sum of two uncertain Fourier amplitudes for a mode.»

The most interesting, maybe, his controversy with Sudarshan:

as well as, in a footnote, with Mandel and Wolf:

Where Ref. 1 is his own Letter.