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Graduate student Steve Zelazny and Professor Koch are inspecting the downstream end of their fast-atomic-beam apparatus that uses CO2 laser-excited hydrogen or helium Rydberg atoms exposed to intense microwave and other fields. Such experiments address questions in quantum chaos and coherent control of strongly driven quantal systems.* |
Quantum mechanics in its Schrödinger form is a wave mechanics, whereas classical mechanics is a study of trajectories in phase space (positions and momenta or angles and actions, etc.); cf., physical (wave) optics vs. em geometric (ray) optics. Semiclassical methods find approximations to the wave mechanical solutions (the former) from the classical paths (the latter). An important, unsolved problem in physics is the general correspondence, or lack thereof, between short-wavelength wave solutions for a physical system and the ray solutions for it. This boundary between quantal and classical physics is especially interesting when the latter is chaotic. The new, interdisciplinary subfield of quantum chaology studies semiclassical, but nonclassical phenomena in quantal systems whose classical counterparts exhibit the transition to chaotic dynamics.
Our experiments on highly excited states of hydrogen, the simplest atom in nature, driven by microwave electric fields intense enough to cause ionization have helped this system to become a paradigm for studies of quantum chaology in a real, physical system. For recent reviews of experimental and theoretical results using a linearly polarized field, see [1,2]. References [3,4] show how changing the polarization of the driving field from linear, to elliptical, to circular, affects the ionization process and can be used to control it.
Our experimental data have been compared with the results of various quantal, semiclassical, and classical calculations by different theorical groups around the world. These comparisons have shown how subtle is the interplay of quantal and classical effects that affect the ionization process; see, e.g., Refs. [1,2,3,5].
Work in our laboratory leads students to master a rich mixture of optical and other experimental techniques. Atoms in a fast beam are created by accelerating and focussing ions extracted from an ion source (examples of the use of charged-particle optics) and passing them through a gas scattering target. Using optical-double-resonance laser-spectroscopic techniques, atoms are raised to highly-excited states using beams from two frequency-stabilized CO2 lasers. These atoms are exposed to strong microwave fields in specially designed and calibrated [6] interaction region(s), an example of microwave optics at work.
Another topic in quantum chaology that is widely studied experimentally and theoretically is the statistics of eigenvalues and the patterns of wavefunctions in quantal billiards. (This is not the familiar (macroscopic) billiards game that uses a rectangular table and three balls. In condensed matter mesoscopic physics the quantal billiards are tiny devices whose boundaries can have various shapes, not just rectangular. They are made by electron beam lithography and use electrons for the "balls".) In two dimensions the Helmholtz eigenproblem for the vector waves of the electromagnetic field confined in a (two dimensional) cavity is mathematically equivalent to the Schrödinger equation eigenproblem for the de Broglie scalar matter waves in a two dimensional quantal billiard. Hence, one can use two dimensional, macroscopic electromagnetic cavities to study mesoscopic quantal billiards. The interesting, challenging wave physics occurs when the shape of the boundary gives nonintegrable (irregular) motion of the trajectories of particle in the classical system. Most semiclassical approaches for obtaining their wave-mechanical properties begin with the classical periodic orbits, but one must also account theoretically for various kinds of wave-diffraction, wave-tunneling, and ray-splitting effects. Besides the microwave domain, this physics also applies to irregular optical resonators and acoustical cavities, e.g., concert halls. Examples of our work on two dimensional electromagnetic cavities are [7,8,9]. We have also obtained results for three dimensional electromagnetic cavities, see [10].
A vast amount of experimental and theoretical research worldwide is directed at developing schemes to control the outcome of photo-initiated reactions of quantal systems when many different outcomes are possible. Given the particular properties (spectrum, decay channels and lifetimes, etc.) of a quantal system, one wants to determine how to drive it preferentially toward the desired outcome by manipulating in time the amplitude-, frequency-, and polarization-, and coherence-properties of electromagnetic field(s) driving it. Our experimental and theoretical research uses a simple quantal system, helium atoms prepared in highly excited (Rydberg) states, driven by microwave field(s). One particularly striking example of the kind of "two-slit" quantal interference effect that one can produce and manipulate is Stueckelberg oscillations. Reference [11] shows how sensitive is this interference effect to variation of the microwave driving frequency and to the amount of broadband noise added to it to decrease its coherence; references [12,13] show how senstive it is to the polarization of the driving field. Reference [14] shows how use of two coherent microwave fields (in this case, both were linearly polarized) gives even greater control. The two-frequency Stueckelberg oscillations we discovered experimentally are also explained well by our theoretical calculations. Ongoing and future experiments, using both helium Rydberg atoms and excited hydrogen atoms [4,15], will extend these methods for even more dramatic coherent control of strongly driven quantal systems.
Prof. P. Koch (e-mail)
Students
Steve Zelazny (e-mail)
Christian Horn (e-mail)
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