Phase Diagrams and Quantum Phase Transitions in Lattice-Confined Antiferromagnetic Spinor Bose-Einstein Condensates

A spinor Bose-Einstein condensate (BEC) confined in optical lattices has attracted much attention for its abilities to systematically study, verify, and optimize condensed matter models. In this dissertation, I present results from three of our recent experimental studies on lattice-confined antiferromagnetic spinor BECs.First, I explain how we have achieved the first experimental realization of the first-order superfluid (SF) to Mott-Insulator (MI) quantum phase transition in lattice-confined antiferromagnetic spinor BECs. Marking an important milestone, a second-order SF-MI transition was realized in scalar BECs about a decade ago. Spinor BECs, on the other hand, possess an additional spin degree of freedom, leading to a range of phenomena absent in scalar BECs. One important prediction is the existence of first-order SF-MI transitions in antiferromagnetic spinor BECs. By adiabatically loading sodium spinor BECs into sufficiently deep cubic lattices, we have observed trustworthy signatures of the first-order SF-MI transitions. These observed signatures include hysteresis effect, significant heatings across the phase transitions, and changes in spin populations due to the formation of spin singlets in the MI phase. We have found the nature of the phase transitions strongly depends on the ratio of the quadratic Zeeman energy q to the spin-dependent interaction. Our observations are qualitatively understood by the mean field theory (MFT), and also suggest tuning q is a new approach to realize SF-MI transitions.Second, we have experimentally mapped the phase diagram of lattice-confined antiferromagnetic spinor BECs at various q and various magnetization. We have also studied the first-order SF-MI transition in different lattice geometries including monoclinic lattices. Good agreements between our experimental results and MFT are observed.Third, we have theoretically proved and experimentally confirmed that combining cubic lattices with spinor BECs substantially relaxes three strict constraints and brings spin singlets of ultracold spin-1 atoms into experimentally accessible regions. A spin singlet of spin-1 atoms has been widely suggested as an ideal candidate in studying quantum information science, because of its long lifetimes and enhanced tolerance to environmental noises. Via two independent detection methods, we have demonstrated that around 80% of atoms in lattice-confined spin-1 spinor BECs can form spin singlets.Photonic