«The term "coherence" has had long if somewhat varied use in areas of physics concerned with the electromagnetic field.»
The Quantum Theory of Optical Coherence. R. J. Glauber in Phys. Rev. 130:2529 (1963). What the paper says!?
The present paper, which is the first of a series on fundamental problems of optics, is devoted largely to defining the concept of coherence.
The fields traditionally described as coherent in optics are shown to have only first-order coherence. The fields generated by the optical maser, on the other hand, may have a considerably higher order of coherence.
He considers general spatio-temporal coherence of the type:
where, note, $x_1\neq x_{n+1}$ in general, i.e., not the same event (spacetime) for creation and annihilation. This is something we didn't take into account with Eduardo.
There is a nice discussion on stationarity and treatment of time (ahead of Eberly & Wódkiewicz's treatment[1]):
A further difference between our approach and previous ones is that it is constructed to apply to fields of arbitrary time dependence, rather than just to those which are, on the average, stationary in time.
It would hardly seem that any justification is necessary for discussing the theory of light quanta in quantum theoretical terms.
The quantum theory, in other words, has had only a fraction of the inQuence upon optics that optics has historically had upon quantum theory.
that the quantum theory is fundamentally necessary to the treatment of these problems is not to say that the semiclassical approach always yields incorrect results. On the contrary, correct answers to certain classes of problems of photon statistics' may be found through adaptations of classical methods.
There are some relativistic elements considering correlations (page 2530) that seem suspicious.
Recording photon intensities with a single detector does not exhaust the measurements we can make upon the field, though it does characterize, in principle, virtually all the classic experiments of optics.
Whatever may be the practical difficulties of more elaborate experiments, we may at least imagine the possibility of detecting n-fold delayed coincidences of photons for arbitrary n.
There is an outdated and typical lack of foresight regarding the future of the field:
The electromagnetic field may be regarded as a dynamical system with an infinite number of degrees of freedom. Our knowledge of the condition of such a system is virtually never so complete or so precise in practice as to justify the use of a particular quantum state $\ket{}$ in its description. [...] Since there is no possibility in practice of controlling these parameters, we can only hope ultimately to compare with experiment quantities which are averages over the distributions of the unknown parameters.
The nth-order function satisfies 2n different wave equations, one for each of its arguments $x_j$, (j= 1,..., 2n).
On statistical independence of the coherent states:
Interesting reference to some M. J. K. Golay, Proc. IRE 49, 959 (1961); also 50, 223 (1962).
To discuss coherence in quantitative terms it is convenient to introduce normalized forms of the correlation functions.
The HBT experiment is seen mainly as proof that one can have first-order (monochromaticity) but not second-order coherence.
Definition of coherence, as factorization of the correlation functions:
«any classical field of predetermined (i.e, nonrandom) behavior has correlation functions which fall into this form, and such fields are at times called coherent in communication theory.»