«I thought I would tell you this morning a few things about [the] century long biography [of the one hundredth birthday of the light quantum].»
Nobel Lecture: One hundred years of light quanta. R. J. Glauber in Rev. Mod. Phys. 78:1267 (2006). What the paper says!?
This is the Nobel Prize lecture by Roy Glauber for his 2005 award, for his inputs in quantum optics. He does not comment much on personal insights, although the whole account is engaging and original:
Of course we have had light quanta on Earth for eons, in fact ever since the good Lord said “let there be quantum electrodynamics”—which is a modern translation, of course, from the biblical Aramaic.
There is a great (and literary) account of the birth of quantum mechanics, Planck's inputs and Einstein's crowning achievement:
It was thus Einstein who fathered the light quantum, in one of the several seminal papers he wrote in the year 1905.
Here we also read about Nadelstrahlung as the «first of the random variables in the quantum theory that began disturbing Einstein and kept nettling him for the rest of his life.»
we described radiation processes in terms that have usually been called “semiclassical.” Now the term “classical” is an interesting one—because, as you know, every field of study has its classics. In physics we are a great deal more precise, as well as contemporary. Anything that we understood or could have understood prior to the date of Planck’s paper, December 14, 1900, is to us “classical.” Those understandings are our classics. It is the introduction of Planck’s constant that marks the transition from the classical era to our modern one.
He then makes a rather personal but compelling point regarding "semi-classical":
The true “semiclassical era,” on the other hand, lasted only about two years. It ended formally with the discovery by Paul Dirac (1927, 1927) that one must treat the vacuum, that is to say, empty space, as a dynamical system.
The countless optical experiments that had been performed by the middle of the 20th century were in one or another way based on detecting only the intensity of light. It may even have seemed there wasn’t anything else worth measuring.
The angular brackets $\langle\cdots\rangle$ indicate that an average value is somehow taken, as we have noted.
When the laser became available, with the knowledge from HBT effect that light from thermal source is temporally correlated, Glauber pondered:
The question then arose: What are the correlations of the photons in a laser beam? Would they extend, as one might guess, over much longer time intervals as the beam became more monochromatic? I puzzled over the question for some time, I must admit, since it seemed to me, even without any detailed theory of the laser mechanism, that there would not be any such extended correlation.
His argument at the time relies on the analogy with classical current and his knowledge from Ref. [1] that «such currents, I knew, emitted Poisson distributions of photons, which indicated clearly that the photons were statistically independent of one another.»
Speaking about coherent states and their knowledge in mechanics by Schrödinger:[2]
Known thus from the very beginning of wave mechanics, they seemed not to have found any important role in the earlier development of the theory.
He refers to the
so-called “diagonal representations” that are quite convenient to use—when they are available
, which seems a nasty wink since Sudarshan showed that they are always available, but later on, he further belabors the point:
It [the P function] cannot be defined, for example, for the familiar “squeezed” states of the field in which one or the other of the complimentary uncertainties is smaller than that of the coherent states.
And he even cites Sudarshan for that statement! It is my understanding that they are available in terms of derivative of $\delta$ functions. He also does not mention Fock states.
There is a nice description of the detection process, which has always been important in Glauber's work.
An interesting observation on the fermion case:
There is a one-to-one correspondence between the mathematical operations and expressions for boson fields, on the one hand, and fermion fields, on the other hand. That correspondence has promise of proving useful in describing the dynamics of degenerate fermion gases.
He concludes with an interesting, personal anecdote:
I’d like, as a final note, to share with you an experience I had in 1951, while I was a postdoc at the Institute for Advanced Study in Princeton. Possessed by the habit of working late at night—in fact on photon statistics (Glauber, 1951) at the time—I didn’t often appear at my desk early in the day. Occasionally I walked out to the Institute around noon, and that was closer to the end of the work day for Professor Einstein. Our paths thus crossed quite a few times, and on one of those occasions I had ventured to bring my camera. He seemed more than willing to let me take his picture as if acknowledging his role as a local landmark, and he stood for me just as rigidly still. Here, in Fig. 10, is the hitherto unpublished result. I shall always treasure that image, and harbor the enduring wish I had been able to ask him just a few questions about that remarkable year, 1905.
He has a typo in the Husimi distribution where he uses $\pi$ everywhere (instead of, twice, $\alpha$).