A Universal Energy Functional for Trapped Fermi Gases with Large Scattering Length

Yoram Alhassid conjectured that the total energy of a harmonically trapped two-component Fermi gas with large scattering length is a linear functional of the occupation probabilities of single-particle energy eigenstates. We confirm his conjecture and derive the functional explicitly. We show that the functional applies to ALL smooth potentials having a minimum, not just harmonic traps. We also calculate the occupation probabilities of high energy states.Comment: 4 page

Confinement-induced p-wave resonances from s-wave interactions

We show that a purely s-wave interaction in three dimensions (3D) can induce higher partial-wave resonances in mixed dimensions. We develop two-body scattering theories in all three cases of 0D-3D, 1D-3D, and 2D-3D mixtures and determine the positions of higher partial-wave resonances in terms of the 3D s-wave scattering length assuming a harmonic confinement potential. We also compute the low-energy scattering parameters in the p-wave channel (scattering volume and effective momentum) that are necessary for the low-energy effective theory of the p-wave resonance. We point out that some of the resonances observed in the Florence group experiment [Phys. Rev. Lett. 104, 153202 (2010)] can be interpreted as the p-wave resonances in the 2D-3D mixed dimensions. Our study paves the way for a variety of physics, such as Anderson localization of matter waves under p-wave resonant scatterers.Comment: 19 pages, 8 figures; published versio

Confinement-induced Efimov resonances in Fermi-Fermi mixtures

A Fermi-Fermi mixture of 40K and 6Li does not exhibit the Efimov effect in a free space, but the Efimov effect can be induced by confining only 40K in one dimension. Here the Efimov's three-body parameter is controlled by the confinement length. We show that the three-body recombination rate in such a system in the dilute limit has a characteristic logarithmic-periodic dependence on the effective scattering length with the scaling factor 22.0 and can be expressed by formulas similar to those for identical bosons in three dimensions. The ultracold mixture of 40K and 6Li in the 1D-3D mixed dimensions is thus a promising candidate to observe the Efimov physics in fermions.Comment: 5 pages, 4 figure

Exact Relations for Two-Component Fermi Gases With Contact Interactions

Presented at the QMath13 Conference: Mathematical Results in Quantum Theory, October 8-11, 2016 at the Clough Undergraduate Learning Commons, Georgia Tech.New Mathematical Topics Arising in Current Theoretical Physics - Monday, October 10th, 2016, Skiles 202 - Chair: Bruno NachtergaeleShina Tan is an Associate Professor in the School of Physics, Georgia Institute of Technology