Polarization and decoherence in a two-component Bose-Einstein condensate

We investigate theoretically polarization properties of a two-component Bose-Einstein condensate (BEC) and the influence of decoherence induced by the environment on BEC polarization through introducing four BEC Stokes operators which are quantum analogues of the classical Stokes parameters for a light field. BEC polarization states can be geometrically described by a Poincaré sphere defined by expectation values of BEC Stokes operators. Without decoherence, it is shown that nonlinear inter-atomic interactions in the BEC induce periodic polarization oscillations whose periods depend on the difference between self-interaction in each component and inter-component interaction strengths. In particular, when inter-atomic nonlinear self-interaction in each BEC component equals inter-component nonlinear interaction, a Stokes vector associated with Stokes operators precesses around a fixed axis in the dynamic evolution of the BEC. The value of the precessing frequency is determined by the strength of the linear coupling between two components of the BEC. When decoherence is involved, we find each component of the Stokes vector decays, which implies that decoherence depolarizes the BEC.