A Bose Einstein Condensate (BEC) is an extraordinarily versatile state of matterthat allows for the simulation of quantum phenomena on the macroscopic scale. This powerful platform features rich physics such as superfluidity, quantum phase coherence, long range order, and spontaneous symmetry breaking. A spinor BEC, or a BEC with a spin degree of freedom, in particular is highly controllable as a quantum simulator, especially under the application of customizable optical lattices. In this thesis I present a study of spinor BECs in moving optical lattices. The results of this thesis open the way for the exploitation of not only quantum based properties of a BEC, but also the classical spatial dynamics inherit to the system for simulating many-body quantum spin dynamics with highly tunable, time-dependent interactions.

First we study the basic physics and construction of a BEC and review the relevant atom light interactions for the application and design of static and moving optical lattices. Then, we experimentally study the spin dynamics of a sodium antiferromagnetic spinor condensate resulting from the competition between the spin-dependent interactions c2 and quadratic Zeeman energy q after the application of a quenched optical lattice. In quenching the moving optical lattice speed, we discover the emergence of violent spatial dynamics within the spatial profile of a BEC. Combined with an analysis of the spin dynamics, we develop a novel understanding of the coherences of the BEC system and the effect of the spatial dynamics upon the spin interactions.

Additionally, we utilize a spinor BEC and its combination of both spin and spatial degree of freedom to construct a quantum simulation experiment of the phenomena of tunneling. Specifically, we experimentally study tunneling in an expanded multi-state system and observe nonexponential behavior due to the presence of a nonlinearity. Finally, I discuss the opportunities for future research using similar dynamic lattice systems investigating the spin dynamics of the dynamic lattice system further.