We have a long-standing theoretical research project on photoassociation and Feshabch resonances in quantum degenerate gases. In these mathematically equivalent phenomena, two atoms combine to make a molecule. Our quantum-optics style modeling starts from a nonlinear field theory for the coupling of atom pairs to molecules. We usually end up solving approximate versions of the theory numerically on a PC cluster that currently has over 100 nodes.

We begun with photoassociation of atoms in a Bose-Einstein condensate (BEC). In the simplest case an atomic condensate is coupled to a molecular condensate only. The macroscopic wave functions of the condensates make a nonlinear counterpart of the usual two-level equations of quantum optics. Correspondingly, we have predicted analogs of coherent optical transients in photoassociation. One such transient, rapid adiabatic passage, is now the quintessential tool in the studies of the Feshbach resonances in both a BEC and a degenerate Fermi gas.

Unfortunately, while momentum conservation and similar considerations dictate that atoms in a condensate must combine into molecules in a condensate, the reverse does not hold; a condensate atom may break up into a pair of correlated noncondensate atoms. We have included this "rogue dissociation" into our modeling. We predict that rogue dissociation gives a limit on the rate of atom-molecule conversion that at low temperatures is more stringent than the unitarity limit of collisions theory. Whether this is the case experimentally remains an open question. We have also modeled both qualitatively and quantitatively the famous experiments on Ramsey fringes observed in Feshbach resonances.

Rapid adiabatic passage can be used to convert a degenerate Fermi gas into molecules. Since fermions cannot be described by a macroscopic wave function, the two-level paradigm that has served as a starting point in our investigations of boson systems must be abandoned at the outset, and new tools need to be developed. We have recently taken the first steps in this direction, and presented a scheme for modeling fermion systems that can semiquantitatively reproduce the experimental findings.

Photoassociation is the inverse of photodissociation, "irreversible" dissociation of molecules into atoms. Our research started with us being curious about how that can be. Nowadays Feshbach resonances in degenerate gases are main area within Atomic, Molecular and Optical physics, with dedicated sessions in major conferences.

It has been known for a long time that fermions sitting on a topologically nontrivial background field may exhibit fractional quantum numbers. For instance, the fermion number operator may have the eigenvalue one half. We have recently noted that a certain (complicated) kind of an optical lattice that is occupied by half a fermion on the average may also produce a fractional fermion. In further work we have clarfied the nature of this half of a fermion, and discussed possible ways to detect it. Presently we are attempting to come up with practically feasible ways of preparing and detecting a fractional fermion optically in an optical lattice. Fermion fractionalization and the closely related spin-charge separation are now a major organizing principle in condensed-matter physics. We hope that atomic-physics realizations could provide new insight and experimental opportunities in this area.

We begun looking into the theory of optical lattices initially as a spin-off of our studies into the phase of a BEC. Our predictions about the loss of phase coherence between the condensates in adjacent lattice sites when the lattice is made stronger have since then been verifice experimentally. In the interim, the prospects of using optical lattices in quantum information system and the intriguing superfluid - Mott insulator transition have spawned an explosive growth in the interest in bosons in an optical lattice. We have gone back to optical lattice systems with the mischievous ambition of finding a way to predict this "quantum phase transition" semiclassically. We now study accelerated or "tilted" optical lattices. The superfluid - Mott insulator phase transition has eluded us so far, but in the course of our studies we have shown that, counterintuitively, a string with condensates in an accelerated lattice tends to become unstable in the limit of *small* acceleration.

last update 2/26/04 by jj