Hans G. Dehmelt The Nobel Prize in Physics

autobiography

The phenomenal accuracies achieved for the spectroscopy of single charged particles suspended in Penning traps has prompted this study of the imperfect Penning trap.

The principal result is a new prescription for the cyclotron frequency in terms of the observable eigenfrequencies of the imperfect trap.

The new prescription is completely insensitive to a misalignment of the magnetic field direction with the axis of the Penning electrodes, and it is also insensitive to the most significant imperfections in the electrostatic potential.

These systematic effects can therefore be completely circumvented in measurements of the anomalous magnetic moments of the electron and positron, and also in experiments on protons and heavier ions where the effects are much larger

Penning traps have long been an important tool for high precision measurements in physics, such as the measurements of the g-factor of the electron and the proton/electron mass ratio. The ideal Penning trap features a spatially uniform magnetic field and an electrostatic quadrupole potential. A charged particle moving in such an ideal trap is a linear system and thus generates harmonic oscillations. It is the accuracy of measuring those harmonic frequencies that determines the accuracy of a measurement. A great deal has been done to minimize the nonlinearity which arises in the actual construction of a Penning trap. In this dissertation, we investigate the possibility of observing chaos in a system of a driven single charged particle moving in a nonlinear Penning trap, in which the nonlinearity is large and not just a perturbation of the linear Penning trap. Our analysis shows that Penning traps may be used as a tool to study the behavior of a nonlinear system. We first suggest a design of a nonlinear Penning trap in which the electrostatic potential would greatly differ from the quadrupole potential. In particular, our design is to generate a strong nonlinear axial potential --the potential along the magnetic field axis. We then discuss the motion of a single charged particle in this nonlinear axial potential. The resultant equation of motion is Duffing's equation which physically describes a damped nonlinear oscillator driven by a periodic force. The dynamical behavior of this Duffing's equation is studied numerically by varying the damping and the driving frequency parameters as well as the amplitude parameter. We finally discuss the possibility of observing chaos in such a nonlinear system. Some chaotic regions in the parameter space are identified.



My father, Georg, had studied law at the Universität Berlin for some years, and in the first World War had been an artillery officer. He was of a philosophical bend of mind and a man of independent opinions. In the depth of the depression he just managed to make a living in real estate. When the family fortunes had shrunk to ownership of a heavily mortgaged apartment building located in an overwhelmingly Communist part of Berlin,

it seemed reasonable to move into one of the apartments ourselves as nobody paid any rent. Cannons were deployed on the streets on occasion and the class war had entered the class rooms. After a few bloody noses administered by a burly repeater, I shifted my interests from roaming the streets more towards playing with rudimentary radio receivers and noisy and smelly experiments in my mother's kitchen. In the spring of 1933 my mother, a very energetic lady, saw to it that, at the age of ten, I entered the Gymnasium zum Grauen Kloster, the oldest Latin school in Berlin, which counted Bismarck amongst its Alumni. This involved a stiff entrance examination and I was admitted on a scholarship. My father at that time expressed the opinion that I probably would be happier as a plumber. However, he apparently didn't quite believe this himself. Thus, in years before, he had bought me an erector set and books on the lives of famous inventors and Greek mythology, and when I was ill he had given me the encyclopedia to read. I supplemented the school curriculum with do-it-yourself radio projects until I had hardly any time left for my class work. Only tutoring from my father rescued me from disaster. Reading popular radio books deepened my interest in physics. While physics was taught at the Kloster only in the later grades, in the public library I read books with titles such as "Umsturz im Weltbild der Physik" and learned about the Balmer series and Bohr's energy levels of the hydrogen atom. My teachers at the Kloster were excellent, I remember in particular Dr. Richter, who taught Latin and Greek, and Dr. Splettstoesser, who taught biology and physics. Richter liked to expand on the classical works, which we were reading in class. I spent most of the ample breaks in related intense discussions with a group of classmates, Heppke, Hubner, Landau and Leiser while others engaged in boxing matches. Splettstoesser was a working scientist who spent Summers as a visitor with a marine biology institute on the Adriatic. I jumped a term and graduated in the spring of 1940.

Having received a notice from the draft board, I found it wise to volunteer for the anti-aircraft artillery and a motorized unit. I was not able to serve as a radio man but was assigned to a gun crew and never rose above the rank of senior private. Sent to relieve the German armies at Stalingrad, my battery was extremely lucky to escape the encirclement. A few months later I was even more lucky to be ordered back to Germany to study physics under an army program at the Universität Breslau in 1943. After one year of study, I was sent to the Western Front and captured in the Battle of the Bulge. I spent a year in an American prisoner of war camp in France and was released early in 1946. Supporting myself with the repair and barter of prewar radios, I took up my study of physics again at the Universität Göttingen. Here I attended lectures by Pohl, Richard Becker, Hans Kopfermann and Werner Heisenberg; Max v. Laue and Max Planck attended the physics colloquia. At the funeral of Planck I was chosen to be one of the pall bearers. At the university, I greatly enjoyed repeating the Frank-Hertz experiment, the Millikan oil drop, Zeemann effect, Hull's magnetron, Langmuir's plasma tube and other classic modern physics experiments in an excellent laboratory class run by Wolfgang Paul. In one of his Electricity & Magnetism classes Becker drew a dot on the blackboard and declared "Here is an electron..." Having heard in another class that the wave function of an electron at rest spreads out over all of space, and having read about ion trapping in radio tubes in my teens set me to wonder how one might realize Becker's localization feat in the laboratory. However, that had to wait a while. In 1948, in Kopfermann's Institute, which was heavily oriented towards hyperfine structure studies, I completed an experimental Diplom-Arbeit (master's thesis) on a Thomson mass spectrograph under Peter Brix. The results were published in "Die photographischen Wirkungen mittelschneller Protonen II," the first paper of which I was a (co)author. Soon thereafter, I began work on my doctoral thesis under Hubert Kruger in the same Institute. Well prepared by a series of excellent Institute seminars on the NMR work of Bloch and of Purcell, we were able to successfully compete with workers at Harvard University. In 1949 we discovered Nuclear Quadrupole Resonance and reported it in our paper "Kernquadrupolfrequenzen in festem Dichloraethylen." My doctoral thesis had the title "Kernquadrupolfrequenzen in kristallinen Jodverbindungen." This work led to an invitation to join Walter Gordy's well known microwave laboratory at Duke University as postdoctoral associate.

At Duke I had the pleasure of making the acquaintance of James Frank, Fritz London, Lothar Nordheim and Hertha Sponer. I advised Hugh Robinson, a graduate student of Gordy's in an NQR experiment, did my own research and also contributed some NMR expertise to an experiment by Bill Fairbank and Gordy on spin statistics in 3He/4He mixtures, gaining some very useful low temperature experience in this brief collaboration. Through Gordy's and Nordheim's good offices I was able to receive a visiting assistant professor appointment at the University of Washington with a charge to advise Edwin Uehling's students during his sabbatical and to do independent research. I had built my first electron impact tube during a brief interlude in 1955 in George Volkoffs laboratory at the University of British Columbia. Prior to that I had attempted a paramagnetic resonance experiment on free atoms in Gottingen and succeeded in doing so at Duke. During seminars at Göttingen on the magnetic resonance techniques of Rabi and of Kastler, it had occurred to me that because of the analogy between an atom and a radio dipole antenna, (a), alignment of the atom should show up in its optical absorption cross section, and (b), electron impact should produce aligned excited atoms. I put these two ideas to good use in 1956 in Seattle in an experiment entitled "Paramagnetic Resonance Reorientation of Atoms and Ions Aligned by Electron Impact." In this paper I first pointed out the usefulness of ion trapping for high resolution spectroscopy and mentioned the 1923 Kingdon trap as a suitable device. This work also brought me into close contact with spin exchange between electron and target atom, which gave me the idea for my 1958 experiment "Spin Resonance of Free Electrons Polarized by Exchange Collisions." However, first I had to learn how to produce polarized atoms, which could then transfer their orientation to trapped electrons. Falling back on buffer gas techniques developed in my 1955 Duke paper "Atomic Phosphorus Paramagnetic Resonance Experiment," I quickly demonstrated in my 1956 Seattle paper "Slow Spin Relaxation of Optically Polarized Sodium Atoms" how to efficiently produce and monitor a polarized atom cloud. Trapping the electrons in a neutralizing ion cloud slowly diffusing in the buffer gas, I was able to carry out the spin resonance experiment. My optical transmission monitoring scheme proved also very useful in the development of rubidium vapor magnetometers and frequency standards by Earl Bell and Arnold Bloom at Varian Associates, in which I acted as a consultant. The rubidium frequency standard is still the least expensive, smallest and most widely used commercial atomic frequency standard. The thesis "Experimental Upper Limit for the Permanent Electric Dipole Moment of Rb85 by Optical Pumping Techniques" of my first graduate student, Earl Ensberg, also made use of these novel optical pumping schemes and was finished in 1962. These early results were improved orders of magnitude by my doctoral student Philip Ekstrom in his 1971 thesis "Search for Differential Linear Stark Shift in Cs133 and Rb85 Using Atomic Light Modulation Oscillators."