Spinor dynamics in a $^{23}$Na Bose-Einstein condensate

Spinor Bose-Einstein condensates (BECs) are characterized by an additional internal degree of freedom, which results in a vector order parameter. In particular, this system may be used to produce an internal state matter-wave amplifier, as well as spin-squeezcd states. In order to pursue these goals it is critical to have an accurate measurement of the spin-dependent interaction energy c$_2$, which is proportional to the difference in scattering lengths a$_{F=2} $ and a$_{F=0}$. The spin-dependent interaction energy determines the ground-state structure as well as the dynamical properties of spinor condensates. A recent result used Feshbach resonance measurements in a BEC to create realistic atomic potentials for sodium and yielded a value which is approximately a factor of two larger than the only measurement in a sodium spinor condensate. Here we discuss the difficulties associated with measuring c$_2$ in sodium, as well as a revised measurement from spinor dynamics. In addition we will discuss our experiments on microwave-dressed spinor states, seeded, and unseeded matter-wave amplification.