Abstract
We investigate amplitude and phase control of the components of the spinor order parameter of a $^{87}\mathrm{Rb}$ Bose-Einstein condensate. By modeling the interaction of the multilevel atomic system with a pair of Raman-detuned laser pulses, we show that it is possible to construct a pulse-sequence protocol for producing a desired state change within a single Zeeman manifold. We present several successful elementary tests of this protocol in both the $F=1$ and $F=2$ Zeeman manifolds of $^{87}\mathrm{Rb}$ using the ${D}_{1}$ transitions. We describe specific features of the interaction, which are important for multimode, spatially varying field configurations, including the role of state-dependent, light-induced potentials.
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