Ultracold Fermi Gases in a Bichromatic Optical Superlattice

Abstract

I describe the theory and construction of a new bichromatic optical superlattice to study the pairing and thermodynamics of spin $\frac{1}{2}$-up and spin $\frac{1}{2}$-down atoms in periodic double well potentials. Our bichromatic lattice contains $\lambda_1=1064$ nm and $\lambda_2=532$ nm standing wave lattices. With tunable depth and relative phase between the two lattices, periodic double well potentials of arbitrary local symmetry can be constructed. I present the first systematic experimental study of a two-component ultracold $^6$Li atomic Fermi gas in a single color 1064 nm lattice, which is continuously tuned from 2D to quasi-2D. A system is 2D if it is free to move in two dimensions while tightly confined in the third direction, such that only the ground state is occupied. Conversely, it is quasi-2D if higher states in the tightly confined direction are also occupied. I describe both radio frequency spectra and radial cloud profiles measured under identical conditions for each regime. Our results confirm predictions that the mean-field theory is not valid throughout the 2D to quasi-2D dimensional crossover. We also clarify that there is no transition between 2D and quasi-2D systems.I also present the first study of pairing in a periodic double well potential. A Green's function method is developed to compute the pairing energies in the lattice. Although further understanding of the results are needed, I provide some preliminary rf spectra measurements supporting the theoretical approach and implying the existence of two types of pairing.