Monday, April 1, 2013

Synchronicity and Quantum Coherent States

Synchronicity was defined as Jung as the occurrence of two unrelated events that combined in the mind of the observer created a significant feeling of connectedness.  For the purposes of physics research, it might be something that belongs in the purview of an institute like Jack Sarfatti's "Physics Consciousness Research Group".  It might also just be explained away as an initial ignorance of the underlying history of the events, kind of like a 'hidden variable' theory.  Keep all these things in mind, as they'll relate to the story below in various ways.

Here are my two seemingly unrelated events.  First, in quantum mechanics this week, we've been assigned a set of problems on coherent states.  Second, my adviser suggested I go to the colloquium being given here at Texas A&M this week by Wolfgang Schleich.  For those of you well versed in physics history, you've probably already gleaned the hidden variables.  For everyone else, read on.

I've been pretty pleased with myself for finding an article[1] a few weeks ago in The American Journal of Physics that has a quite clear explanation of how to derive and use coherent states.  At the end of the article, there was a reference to an article by the same authors with further details that was printed in Physical Review Letters[2].  Reading this article, it became clear that while Carruthers and Nieto had provided an excellent explanation of coherent states, what they were really interested in was their relation to phase operators.  Carruthers and Nieto quoted Susskind and Glogower as doing some of the early work in the field.

I have yet to find the article by Susskind and Glogower in the journal Physics.  According to one of the contributors at StackExchange, it appeared in the same volume that printed the original article about Bell's inequality.  I was also able to find an article at Nuovo Cimento by someone named Jack Sarfatt that referenced it.  The truly handy link from StackExchange was to an article written in 1993[3] by Nieto that explained Susskind and Glogower's work.  This is the paper that connected my two events and made everything clear!

As it turns out, part of the reason that Carruthers and Nieto gave such a clear derivation of coherent states is because the phase operator research sprung from Carruthers proposing it as a homework problem!  Susskind, Glogower and Sarfatt were three of the students who took up the problem. Nieto's article also revealed that Jack Sarfatt was in fact Jack Sarfatti.  He changed his name and added the i at some point.  One of the many colorful things that Sarfatti did in his career was to take umbrage at not being included as an author on Susskind and Glogower's article.  There's quite a bit more detail in Nieto's article, (it's open access on arXiv by the way).

So, we pretty much have the homework problem side of this covered, but where does the second event about the colloquium come in?  About half way through the article, Nieto thanks none other than Wolfgang Schleich for encouraging him to write it!

As an interesting bibliographical aside, (Who am I kidding?  This whole post is a bibliographical aside!), in 1968, Carruthers and Nieto wrote a rather complete review of the field of quantum mechanical phase operators including an interesting discussion of their application to superfluids.  

1.  AJP article from Carruthers and Nieto
Carruthers P. (1965). Coherent States and the Forced Quantum Oscillator, American Journal of Physics, 33 (7) 537. DOI:

2.  PRL article from Carruthers and Nieto
Carruthers P. & Nieto M. (1965). Coherent States and the Number-Phase Uncertainty Relation, Physical Review Letters, 14 (11) 387-389. DOI:

3.  Nieto reveals all in Los Alamos Preprint (open access version from arXiv)
Michael Martin Nieto (1993). Quantum Phase and Quantum Phase Operators: Some Physics and Some History, Phys.Scripta T48:5,1993, arXiv:

4.  Carruthers and Nieto review of quantum phase operators
CARRUTHERS P. & NIETO M. (1968). Phase and Angle Variables in Quantum Mechanics, Reviews of Modern Physics, 40 (2) 411-440. DOI:

5.  Google Books on finding the Susskind and Glogower aritcle

6.  StackExchange on finding the Susskind and Glogower article

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