Melvin Lax

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Interviewed by
Joan Bromberg
Interview date
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Interview of Melvin Lax by Joan Bromberg on 1986 February 6, Niels Bohr Library & Archives, American Institute of Physics, College Park, MD USA,

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Lax has worked on laser theory and the theory of laser noise. Discussion of organization of theoretical group at Bell Laboratories; the path by which he was led to do research on fluctuation theory; his knowledge of engineering theory; and aspects of his work on maser noise.


I had my first job offer from Bell Telephone Laboratories two years before I actually went there. It came from a physical electronics group under Kenneth McKay. It was not a field, in which I had been working, and although they told me that I could do anything I wanted, I did not believe I would have sufficient freedom. In addition, the salary did not match my anticipated annual earnings at Syracuse University; I turned the offer down.

Two years later, John Hornbeck offered me a position in the semiconductor group. William Shockley and John Bardeen had both worked in this group before they left. This time it was my own field of interest I could take a leave of absence from Syracuse University and decide later whether I wished to remain at Bell. There was no risk to coming. A key point, here, was whether the Bell promise of freedom to pursue my own choice of research topics would be fulfilled. It was.

During that year, William O. Baker, then an executive director, in the research area asked a group of us "What can we do to improve the hiring and retaining of first class theorists?" We suggested forming a theoretical physics department. The laboratory had no real theoretical group at the time. Five of us formed the original group. Four were rather experienced physicists, Conyers Herring, Gregory Wannier, Phil Aderson, and I. Peter Wolff, the fifth, was then a younger person.

One of our first moves was to set up a program of "postdoctoral" appointments. The plan was to bring people in for 2 years, and if we liked each other, to invite them to stay permanently. It was designed to be the equivalent of an assistant professorship. At the start it did have the benefits, like life insurance, that are part of the university situation. Jim Phillips was our first postdoctoral fellow. Our second was John Hopfield. We appointed extremely good people, one every two years. They received lots of offers, however, and most did not to stay. I therefore made the suggestion, which was accepted, that we hire 3 at a time. This included such people as Bill Brinkman, Marvin Cohen, Maurice Rice, Bert Halperin and Pierre Hohenberg. (We held a rotating chairmanship of the group, and this was in the 1960s, during my stint as chairman.) One would be sure to leave, one we would not want, and the third would stay. This was not an inordinate amount of hiring at the time, since our group had been growing very slowly. From this later group all but Marvin Cohen stayed past the postdoc period. But we later lost Rice to Zurich and Halperin to Harvard. Brinkman became a high level administrator at Bell of Sandia.

We did not make any particular effort to choose topics in line with Bell's communications mission. I believed that if you get a group of first-rate people together, they would not only do good science, but important science. And important science was not only beneficial for science, but, necessarily, for Bell also. Management did not supervise our choice of problems, but you must keep in mind that only a small proportion (less than 10%) of BTL staff was in the research area.

I first got involved in fluctuation theory in a small way in the 1950's. I had a student at Syracuse University who was attempting to calculate polaron mobility in the 1953-54 periods using a formula I developed for this purpose. I did not talk about this work publicly until a meeting of the American Physical Society [Phys.Rev. 100, 1808, (1955)], and a many-body conference at Stevens Institute of Technology in 1956. A detailed account, called "Generalized Mobility Theory" was published in the Physical Review (Vol. 109, 1921-1926, 1958). The principal result of this paper, the mobility formula came to be known as the Kubo formula. He had developed it independently, at the same time, but made more application of it, and deserves the credit. (He was always very generous in referring to my contribution.) A corollary result was a new derivation of the connection between mobility and (Nyquist or Johnson) noise.

As an aside, I recall that at that time, the Physical Review was being criticized for its editor's slowness. I understood the reason for that slowness when the editor, Pasterank, phoned me to point out some small inconsistencies in my mobility article, and learned that he was personally reading my papers and presumably many others!

As a result of this article, the editors assumed (incorrectly) that I was an expert on noise and began to send me papers on noise in semiconductor devices to review. These were experimental papers which typically employed crude theoretical models. They were all on non-equilibrium situations, where the systems were driven through an applied voltage, a current, or what have you. I would read them and be unhappy. I interacted with an experimentalist at Bell, Harold Montgomery, at this point. Nobody had a systematic approach to the problem. After 5 or 6 such papers, I decided to do something myself.

The result was the paper "Fluctuations from the Non-equilibrium Steady State", [Rev. of Mod. Phys. 32, 25-64, (1960). I chose the Reviews of Modern Physics because I reviewed the whole literature as well as making my own contribution. The basis of my work there was a generalization of the Onsager regression hypothesis.

The familiarity with engineering theory that you mention as a component of these and other papers reflects, in part, the fact that I started my graduate work at MIT during the World War II years. There was some pressure to teach us things that would enable us to quickly be in a position to contribute to war research. As a consequence, I was given two engineering courses. One was advanced network theory with Guillemin. I had never had elementary network theory, but they told me that I had the mathematical background to handle the advanced course. I was able to further deepen my engineering background later, through some of my collaborations. My work with H. P. Yuen was important here; he taught me classical communication theory and I taught him quantum mechanics in the course of developing his PhD thesis on quantum communication theory.

At the time of my 1960 fluctuations paper, I was not yet involved in work on light fluctuations. I did not, for example, attend the 1960 Rochester Conference on Coherence, and would not have expected to have been invited since I had written nothing in the field. In the early 1960s, however, it became readily apparent to me that lasers were an important subject. I was talking to laser people at Bell like J. P. Gordon, R. L. Fork and M. A. Pollack. So I began the work that led to "Formal Theory of Quantum Fluctuations from a Driven State" [Phys. Rev. 129, 2342-2348, (1963)]. That paper is now designated Quantum Noise II (the paper on mobility theory is Quantum Noise I).

I was, by the way, in Oxford in 1961-1962 when Willis Lamb was professor of theoretical physics and we talked about laser theory. We did not work together in any sense, since we were taking extremely different paths, but the fact that we came out with the same results later by very different methods enabled us to know that we each were right. When Lamb moved from Oxford to Yale, he consulted for Bell Telephone Laboratories, so that I continued to see him. On these trips he would talk with Fork and Pollack, as well as with me. I did not have this kind of relation with Haken, although I did see him for example, at conferences. He was at the Puerto Rico conference in the summer of 1965.

For the Puerto Rico conference, it was appropriate to do a short paper. Although I had a draft of the long Quantum Noise IV paper, I decided to present an application to the calculation of line width. This was the first time I had tackled line width. At this time, I came to understand the fact that the line width is proportional 2/P well below threshold, and 1/P well above (when P is the laser power). I did not yet see how the two behaviors were joined, although it was obvious that they must connect. The recognition of the two regimes was important; before this people has been arguing about the 1/P vs. 2/P dependence without realizing that each was valid in a different region. (I did not know Blaquiere and Grivet or Mullen and Golay's work at the time. I went back and dug out their papers after I had already started my own work on line width.) Later, in a paper with Hempstead, we derived the behavior that connected 1/P with 2/P as the mode passed through threshold. [This was his Master’s Thesis at MIT in 1955, published later in Phys. Rev. 161, 350-366, (1967)].

Another important idea in the Puerto Rico paper was the introduction of non-commuting Langevin noise sources. In fact, Haken contributed a paper to that conference using commuting Langevin sources. The editors of the conference proceedings did me a disservice by not printing Haken's result after it became clear that the correct formulation required noncommutativity.

I don't recall exactly how I came to work with McCumber in deriving in a more fundamental way the rate equations that he used. [M. Lax, "Quantum Noise VII: The Rate Equations and Amplitude Noise in Lasers," Joun. Quant. Electron. 3, 37-46, (1967)]. I should point out, however, that there were not so many people working on the theory of lasers, and hence on rate equations, at BTL. McCumber was one of a few.

I knew Leonard Mandel well through the circumstance that I had a daughter attending Rochester University. I would drive her up to school and then drop in on Leonard to chat about work. This interaction shows up in some of my papers. My paper (with Cantrell & Smith), "Third and Higher Order Intensity Correlations in Laser Light", Phys. Rev. A7, 175-181, (1973) compared my theory with his experimental results. My work with Zwanziger, "Exact Photo count Distribution for Lasers near Threshold", Phys. Rev. Letter 24, 937-940, (1970) stimulated Mandel and his group to perform the associated experiments. The full paper [Phys. Rev. A7, 750-771, (1973)] made a detailed comparison between his experimental results and our theory.

Of course, I knew Hans and Freed, and Armstrong and Smith. I should point out, however, that in my relations with experimentalists, they do not suggest the actual ideas for advancing the theory. They would not suggest an idea, for example, like using non-commuting noise sources, because their treatments are more intuitive and unlikely to lead to new formalism. My interaction with experimentalists is to follow their work and to compare their data with my results. I can come back from a conference with 25 new ideas, but not in the form of concrete suggestion for the next step. (Jim Gordon is an exception to these comments. At least one of his papers is as deep as any theorist's. I have had many cordial and useful conversations with Gordon.)

Since coming to CCNY, I have done some consulting for the Army. This has pushed me in the direction of considering more practical problems, like the distribution of fields inside lasers. I have also been consulting at BTL with the principal emphasis on nonlinear interactions of light and sound in crystals, and more recently semiconductor physics.