The field of quantum gases or ultracold atoms is the fastest expanding and most interdisciplinary field in physics today. The experimental branch of this exciting new field uses the techniques of atomic, molecular, and optical physics to study many-body systems consisting of extremely cold trapped atoms. These are condensed matter systems whose constituents have well-understood microscopic interactions. At sufficiently low temperatures, the large de Broglie wavelengths of the atoms allow these systems to exhibit quantum phenomona on a macrosopic scale. The theoretical branch of this field is completely interdisciplinary, attracting top scientists from atomic, condensed matter, high energy, and nuclear physics as well as from quantum optics and quantum information. The Cold Atom Physics group at OSU has established itself as one of the world's top theory groups in this area.
I will discuss elastic and inelastic collisions in a gas of weakly bound homonuclear and heteronuclear molecules composed of fermionic atoms and show that such molecules represent novel composite bosons, which exhibit features of Fermi statistics at short intermolecular distances. I will also discuss Bose-Einstein condensation of these composite bosons and outline prospects for future studies of Fermi mixtures with different masses.
We develop a functional integral formalism for ultracold fermionic gases which exhibit the BEC-BCS crossover. Our formalism involves both atom and molecule fields, coupled via a Yukawa or Feshbach coupling. In this talk the universal aspects of the crossover problem will be underlined. Special attention is paid to the universality obtained in the narrow and broad resonance limits (small and large Feshbach couplings, respectively). For the narrow resonances, an exact solution of the many body problem is established. In the broad resonance case, a strongly coupled fermion system with pointlike microscopic interaction is approached. The "dressed molecules" in the BEC regime macroscopically exactly behave like weakly interacting fundamental bosons as described by a standard Bogoliubov theory. Our results agree with Quantum Monte Carlo simulations performed at the resonance. Our findings for the "bare molecules" fit with a recent experimental study.
We show that the Lagrangian for interacting nonrelativistic particles can be coupled to an external gauge field and metric tensor in a way that exhibits a nonrelativistic version of general coordinate invariance. We explore the consequences of this invariance on the example of the degenerate Fermi gas at infinite scattering length, where conformal invariance also plays an important role.
A number of experimental groups have been highly successful in using scattering resonances known as Feshbach resonances to control the dynamics of cold quantum gases. Tuning the resonance with a magnetic field allows precise control of the scattering length as well as the production of ultracold molecules for both bosonic or fermionic atomic species. For example, extremely large molecules of the Li-6 dimer with mean interatomic separation larger than 100 nm can be made, Bose condensed, and quantitatively probed by radiofrequency photodissociation. This talk will introduce simple models based on full quantum scattering calculations to examine the characteristics and properties of such resonance states and molecules.