This research project will lead to understanding and control of the dynamics of quantum systems, including but not limited to electrons escaping from atoms, trapped atoms, ultracold gases, and molecules. Control of quantum systems -- electrons, atoms and molecules is one of the 'grand challenges' of modern physics. This research cuts across many disciplines in physics, mathematics and chemistry. Microscopic quantum systems can be understood and controlled by understanding and controlling the analogous macroscopic classical systems. New discoveries in classical mechanics can be used to show how to obtain similar control over quantum systems. For example, the theory of chaotic transport was first introduced to study systems of three bodies interacting under gravity, and has more recently been used to design spacecraft trajectories, examine orbits of comets, study transport of meteors from Mars to the Earth, and learn about mixing in fluids. It will be used to study escape of atoms from cavities, escape of electrons from highly excited atoms, and transport of atoms through nanojunctions. These are systems which have only a few degrees of freedom, for which the interparticle forces are known and controllable, and on which precise measurements can be made. This research is also connected to technology. The mechanisms of escape of electrons from atoms is similar to the mechanisms of escape of electrons from nanojunctions ('designer atoms') and similar to the mechanisms of escape of photons from optical resonators. In addition, highly excited states of atoms can be used as infrared detectors, and chaotic ionization processes have been used to make a streak camera. The field of nonlinear dynamics is excellent for introducing students to research. As soon as students learn elementary aspects of Newton's Laws, they can begin computing trajectories, and analyzing their structure.
A new phenomenon in classical and quantum integrable systems called monodromy will be studied. Also new phenomena associated with pumping ultracold atoms from one reservoir to another, 'Ballistic Atom Pumps', has been discovered and will be further explored. Computations predicting future observations of the 'tennis-racket flip' in isolated molecules will be carried out. Finally dynamical control theory will be applied to understand respiration in premature infants. For example, it is believed that periodic apneas occur when time-delays in a control loop throw the system into oscillation; this theory will be compared with data provided by University of Virginia.
