Spin Orbit Coupling in a Spin-1 System*

Using a three frequency Raman coupling scheme, we create a system that provides independent control of the bare energy states of a spin orbit coupled $^{87}$Rb Bose-Einstein Condensate in the $F=1$ hyperfine state. The independent energy level control given by the three frequency coupling scheme leads to tunable effective quadratic Zeeman shift which is used to create a spin-1 spin orbit coupled system. In this work we study the energy dispersion under various spin orbit coupling and effective quadratic Zeeman shift magnitudes. In addition, we explore the modified many-body interactions in the spin orbit coupled system.