Reminiscing about thesis work with E T Jaynes at Stanford in the 1950s

Abstract A short personal and historical account of the field of radiation interacting with (two-level) atoms is given. Subsequent to 1963, developments and extensions have been extensive and fruitful. One of the most fortunate changes in my life came in late 1957. I was looking for a thesis advisor, after two years of graduate course-work at Stanford. I chanced to see a notice of an upcoming lecture by a professor named Edwin T Jaynes. I could not understand from the announcement what he intended to talk about, but I was searching; I went to find out. That decision was a very lucky one. Ed was talking about a subject that inspired him then, and had been for many years, namely his concept of 'Max-Ent'. 'Maximum-Entropy' is a subject now close to my heart also. Ed's very-clear, well-thought-out papers, spread over many subsequent years, are transforming the field of probability (albeit too gradually) to the 'subjective' outlook of Bayes. (A recent book 'Maximum Entropy and Ecology' [1] will probably convert many nay-sayers to 'Max-Ent'.) I went into Ed's office (late 1957) and asked if I could work with him on a thesis. Did he have a problem for me? Yes, he did. Somewhat to my surprise, he asked me to look into the 'maser problem', involving a comparison of the semi-classical theory of radiation to a proper quantum treatment. To make a two-year story short, Ed's guidance was expert. (I imagine that if another of Ed's students (e.g. Joe Eberly) had come into his office fifteen minutes before me, the 'Jaynes–Cummings' (J–C) model would now perhaps be called otherwise, e.g., the 'J–E' model). In the two-year time frame (~1958–60), Ed had a number of other PhD dissertation students whom I knew; these included Joe Eberly, Doug Scalapino, Baldwin Robertson, Larry Davis and Mike Duggan. My thesis work under Ed reminds me of a story about Michelangelo and his famous 'Pieta'. Michelangelo was an old man about then, so he hired a young craftsman to do much of the physical work: 'chip here, carve there, cut off here, eliminate this, etc'. When the beautiful Pieta was finished, the young man was heard to say, 'I didn't realize before this that I was so talented'. Experiments by Clauser in 1972 on Bell's inequalities (e.g. [2]) showed them to be correct, and indicated that semi-classical alternatives to quantum electrodynamics were not viable. Working with Stuart Freedman, these were the first experimental tests of the predictions of Bell's theorem, the first observation of quantum entanglement, as well as the first experimental observation of a violation of a Bell inequality. The perturbation formulation of quantum radiation theory has long been rife with vexing infinities. Ed always insisted that only experiment can end an argument, so he and his students had been sensibly exploring semi-classical theory. This was not only because of the serious failings of standard QED, but more importantly because of the fact that (an improved) semi-classical theory was able to predict both spontaneous emission, with the correct Einstein coefficients, and the Lamb shift. These two effects have long been thought only possible in the quantum radiation domain (cf [3]). Ed readily accepted losing his bet with Franken about what experiment had to say about the Lamb shift. What is clear is that this bet of $50 with Peter Franken stimulated so much subsequent research that this bet played an important role in generally furthering the field of quantum optics. How did 'J–C' come to be published as it did in the IEEE [4]? Ed was not well known for the extravagant use of words, rather for paucity, clarity and economy. After about two years of working with Ed, he said to me one day, 'You have enough, write it up'. He also said 'We should publish'. (This was around early 1960). About this same time, I was contacted by someone from a new research lab just starting in Newport Beach, California (called 'Aeroneutronic', a division of Ford), asking if I would come to work there. I thought it sounded about right as an approximately two–three year position: repay some debts and look around at other possibilities (especially academe?). I left around June 1960 to take up this position in the research lab in Newport Beach. At about this same time (~late 1959), Ed was moving to his new 'chair' at Washington University in St Louis. I proceeded as quickly as I could to put together a thesis after arriving in Newport Beach; I wrote about what I had done, as best as I could in my naivete about such undertakings. I wrote of the work I had done under Ed's kind and patient guidance for the two years in Palo Alto. I soon remembered that Ed had done a recent Stanford Microwave Lab report on our project; his writing was so much better than mine that I thought it witless to put out something as 'uneven' as I had written by then. At just this time that I was cobbling together a thesis, a consultant at Aeroneutronic, Jay Singer of UC Berkeley EE department, approached me in the hall, (no tele-commuting then!) asking if I might have something to contribute to a special issue of a journal of the IEEE he was editing, on the subject of 'Quantum Electronics'. (Comment: One of the earliest predecessors to the MRI, Jay Singer was then measuring the blood flow in rat tails and human arms; he holds two key MRI patents). I said I thought I did have something. The journal sounded appropriate, so I soon handed my 'thesis' to Jay, put Ed's name first (of course, since it consisted so largely of his words from the Microwave Lab report, but also since Ed was my 'guru'), ...and that was that...done [4]. From my perspective, it seemed to subsequently sink to the bottom of the sea, not to be seen by me again for many years until the elegant Walther–Rempe–Klein (WRK) experiments of 1987 on long-time coherent radiative behavior appeared [5]. They confirmed the long-time quantum-theoretical results of Eberly, Narozhny and Sanchez-Mondragon [6]. Bob Buley and I, while at Aeroneutronic, had published in the field of lasers [7], based on the J–C model. We found very strange, puzzling 'chaotic' output of a 'Q-switched' laser. When computer time-steps were changed, the chaos didn't disappear. It was about then (~June 1963) that both Bob and I headed elsewhere: I to the early-forming UC Riverside Physics Department as Assistant Professor, and Bob to a company in Santa Barbara. Our work on the mysterious 'chaotic' laser effect then ended (the term 'chaos' was not yet in the physics lexicon); Bob was the computer expert, our non-linear laser problem demanded rigorous numerical computations, and I was not savvy with the (then) 'refrigerator-sized' computers at UCR. P W Milonni has greatly extended this work (cf [8]). Mike Tavis, my graduate student at UCR around 1965, extended the J–C model to N atoms [9]. (We have more recently collaborated in a further study of this and other extensions of J–C.) The silence and zero feedback from the 'J–C', Buley and 'T–C' papers for so many years following 1965 was a bit deafening, so I thought it would be best that I go mostly onto other topics. One day in about 1989, I got a tap on the shoulder from a colleague at UCR: 'I saw your name in the title of a paper'. ('Huh?'). An astonishing number of exciting and important new topics have emerged since the 1987 WRK experiment, providing an ever-branching tree of both new theory and experiment. It is tempting to entitle this piece as 'Get your name in print: Diagonalize a 2 × 2'. References [1] Harte J 2011 Maximum Entropy and Ecology: A Theory of Abundance, Distribution, and Energetics (Oxford Series in Ecology and Evolution) (Oxford: Oxford University Press) [2] Freedman S J and Clauser J F 1972 Experimental test of local hidden-variable theories Phys. Rev. Lett. 28 938 [3] Stroud C R Jr and Jaynes E T 1970 Long-term solutions in semiclassical radiation theory Phys. Rev. A 1 106 [4] Jaynes E T and Cummings F W 1963 Comparison of quantum and semiclassical radiation theories with application to the beam maser Proc. IEEE 51 89 [5] Rempe G, Walther H and Klein N 1987 Observation of quantum collapse and revival in a one-atom maser Phys. Rev. Lett. 58 353 [6] Eberly J H, Narozhny N B and Sanchez-Mondragon J J 1980 Periodic spontaneous collapse and revival in a simple quantum Phys. Rev. Lett. 44 1323 [7] Buley E R and Cummings F W 1964 Dynamics of a system of N atoms interacting with a radiation field Phys. Rev. 134 A1454 [8] Milonni P W, Shin M-L and Ackerhalt J R 1987 Chaos in Laser–Matter Interactions (Singapore: World Scientific) [9] Tavis M and Cummings F W 1968 Exact solution for an N -molecule—radiation-field Hamiltonian Phys. Rev. 170 379