Using a Feshbach Resonance to Study Ultracold Atoms in a 2D Optical Trap

Azure Hansen, Pierre Cladé, Changhyun Ryu, Anand Ramanathan,
Kristian Helmerson, William D. Phillips

National Institute of Standards & Technology, Atomic Physics Division, Laser Cooling Group

Ultracold atomic systems, including Bose-Einstein condensates, can be used to study quantum interactions and phenomena first described in condensed matter physics. Such systems have the advantage that the important parameters of the system are easy to control experimentally. One such parameter is the interaction between atoms, given by the scattering length. A Feshbach resonance permits the scattering length of atoms to be tuned by changing an external magnetic field. We are interested in studying ultracold atoms in a 2D geometry using the Feshbach resonance.

The effective interaction is changed when there is coupling between the quasi-bound and free states of atoms with multiple hyperfine states. This occurs only when the energy of the two states is degenerate, a condition that is achieved by tuning the external magnetic field to the Feshbach resonance. For sodium, this resonance is typically at 1000 G with a width of ~1 G or less. Therefore, a homogeneous and stable magnetic field is required for observing the resonance.

In a 2D system, thermal fluctuations destroy long-range coherence, preventing a BEC from forming. In the Berezinskii-Kosterlitz-Thouless phase, there exists long-range phase coherence, permitting a superfluid quasi-condensed state. The BKT transition is marked by the formation of paired vortices of opposite helicity. The coupling constant g describes this phase transition.

In the quasi-2D geometry, the interactions are described by the dimensionless coupling constant g that depends on the scattering length and the vertical confinement. Previous experiments with cold atoms were in a regime where g<1. Using a Feshbach resonance, we should be able to study the regime where g~1. This is especially interesting because there exists no precise prediction of the transition temperature.

Our experiments use ultracold or Bose-condensed sodium atoms. We create a magnetic field on the order of ~1000 G using a pair of high-current coils in the Helmholtz configuration. The coils can be switched by an IGBT system to anti-Helmholtz configuration for other aspects of the experiment. We trap the atoms in a sheet of light to create the requisite 2D system. Characteristics of the BKT phase such as vortices and coherence properties can be measured using optical imaging or Bragg interferometry.