We develop a cumulant based formalism to deterministically calculate the lowest order quantum fluctuations of a two-component Bose-Einstein condensate. We use this to study spin squeezing induced by the atom-atom interaction nonlinearity. Our formalism naturally accounts for the multimode spatial description of the condensate, extending previous spin squeezing work which assumed a single spatial mode. We study spin squeezing in both the miscible and immiscible (phase separating) regimes for the scattering lengths. In the miscible regime, we find the squeezing parameter deviates very little from the single spatial mode approach, while in the phase separating regime, we find the squeezing is slightly reduced, though significant squeezing still occurs.

• Received 13 November 2006

DOI:https://doi.org/10.1103/PhysRevA.75.023618