Theory of Atomic Motion in Resonant Radiation.

Atomic motion in resonant and near resonant electromagnetic radiation is investigated theoretically. The exposition begins with a study of atomic motion in a resonant standing light wave, with a view toward isotope separation by selective photodeflection, and proceeds to the investigation of more general problems of atomic motion in resonant radiation. The body of the work consists of six chapters, each of which was prepared as a manuscript for publication in the open literature. The Schrodinger equation for atomic motion in a resonant standing wave is solved in Chapter 2 in the limit of short atom-field interaction time. It is shown that momentum transfer from the field to the atom in a standing wave proceeds at the rate of induced absorption -emission processes rather than at the spontaneous rate characteristic of momentum transfer in a plane running wave. The resulting rapid deflection process in a standing wave leads to atomic deflections of sufficient magnitude for isotope separation in a time less than the natural lifetime of the excited atom, and hence circumvents the problem of metastable state trapping encountered in attempts to separate isotopes using a running wave. In Chapter 3 it is shown that a narrow beam of two-level atoms is split by the amplitude gradient of a resonant electromagnetic wave (optical Stern-Gerlach effect), and an experiment is proposed to test this fundamental feature of the resonant interaction. In Chapter 4 it is shown that an exact solution to the Schrodinger equation for atomic motion in a resonant standing wave can be written in terms of Mathieu functions, and that the theory is readily generalized to include the case in which N atomic levels take part in the resonant interaction. A formal analogy between the problem of atomic motion in a standing light wave and diffraction of light by ultrasound is also discussed in this chapter. An alternative approach to the theory of atomic motion in an electromagnetic wave, based on Ehrenfest's theorem and the optical Bloch equations, including effects of spontaneous emission and detuning of the applied field is developed in Chapter 5. The utility of this theory is illustrated by application to the problems of atomic trapping and cooling by the radiation force. The simplicity of calculations in this chapter show that the Ehrenfest-Bloch equations provide a convenient and fruitful framework in which to study such problems. In Chapter 6 the Ehrenfest-Bloch formalism is generalized to take account of laser phase fluctuations and the associated finite linewidth of laser radiation. It is found that fluctuations of the laser radiation alter the predictions of the monochromatic theory only when the laser linewidth approaches or exceeds the natural linewidth of the resonant transition, a situation not usually encountered in practice. Finally, in Chapter 7, the influence on atomic motion of quantum -mechanical fluctuations of the radiation force is investigated. It is shown that fluctuations of the radiation force result from interaction of the fluctuating atomic dipole moment with the applied field as well as from random recoils accompanying spontaneous emission. Atomic motion in the fluctuating radiation force is described by a Fokker-Planck equation, and this equation is used to show that quantum fluctuations place a lower bound on the temperature achievable by radiation cooling, and lead to finite, often short, confinement times for atoms in radiation traps.