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Self-induced Spatial Dynamics to Enhance Spin-Squeezing via One-Axis Twisting in a Two-Component Bose-Einstein Condensate

We theoretically investigate a scheme to enhance spin squeezing in a two-component Bose-Einstein condensate (BEC) by utilizing the inherent mean-field dynamics of the condensate. Due to the asymmetry in the scattering lengths, the two components exhibit density oscillations where they spatially separate and recombine. The effective non-linearity responsible for spin squeezing is increased by up to three orders of magnitude when the two components spatially separate \cite{treutlein2010}. We perform a multi-mode simulation of the system using the truncated Wigner method, and show that this method can be used to create significant spin squeezing in systems where the effective nonlinearity would ordinarily be too small, and that strong spatial dynamics resulting from large particle numbers aren't necessarily detrimental to generating spin-squeezing. We develop a simplified semi-analytic model that gives good agreement with our multi-mode simulation, and will be useful for predicting spin-squeezing in a range of different systems.