Probing Atom On-site Interactions in an Optical Lattice

Abstract

In this thesis, we observe and characterize both s-wave and p-wave interactions of fermionic 40K atoms in deep optical lattices. The p-wave interactions especially draw our attention, as they have a well understood connection to topological properties. The discovery of p-wave interactions in ultracold-atom systems is promising, as the systems are tunable and controllable, but the experimental efforts have been severely limited by the short lifetime of atoms due to the three-body loss mechanism. The deep lattice potential applied in our study ensures near-zero tunneling, such that we are able to directly measure the on-site interaction energies of isolated pairs of atoms, and this isolation especially helps to suppress three-body losses for p-wave interacting pairs.For s-wave interactions between two lowest spin states in the ground hyperfine manifold, the binding energies of the s-wave molecular dimers have been studied pre- viously. However, in our study, we also measure the repulsive interaction energies via the radio-frequency (RF) spectroscopy. The obtained energy eigenspectrum for the atom pairs can be well explained by the theory based on two atoms in a harmonic trap interacting via a pseudopotential. Another experimental technique to measure the s-wave interaction energies is developed as well using Raman excitation. By cou- pling both spin and motional degrees of freedom, we obtain an energy spectrum that agrees well to the one using RF spectroscopy. To study p-wave interactions between two identical atoms in a spin triplet state, we prepare an initial non-interacting triplet state with a motional excitation via Raman excitation, and then directly measure the p-wave interaction energies by RF coupling the initial state to the final interacting one. The resulting universal energy spectra obtained at various conditions are well characterized by an exact solution for two harmonically confined atoms interacting via a p-wave pseudopotential with anharmonic corrections. We also measure the Rabi oscillations of the p-wave interacting pairs, and take the first steps towards the coher- ent control of the oscillations. Finally, we set up an experiment to test the lifetime of the p-wave interacting pairs, and find that losses are limited by the intrinsic lifetime of the molecular dimer. The lifetimes are measured to be much longer than observed for free-space dimers, and are predicted well by calculating the short-range fraction of the wavefunctions. Another theory based on an ab initio interaction potential is applied as well, which gives similar results to the pseudopotential theory, and again proves their validity.