Effective non-linear spinor dynamics in a spin-1 Bose-Einstein condensate

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We derive from first principles the experimentally observed effective dynamics of a spinor Bose gas initially prepared as a Bose–Einstein condensate and then left free to expand ballistically. In spinor condensates, which represent one of the recent frontiers in the manipulation of ultra-cold atoms, particles interact with a two-body spatial interaction and a spin–spin interaction. The effective dynamics is well-known to be governed by a system of coupled semi-linear Schrödinger equations: we recover this system, in the sense of marginals in the limit of infinitely many particles, with a mean-field re-scaling of the manybody Hamiltonian. When the resulting control of the dynamical persistence of condensation is quantified with the parameters of modern observations, we obtain a bound that remains quite accurate for the whole typical duration of the experiment.
effective non-linear evolution equations, many-body quantum dynamics, spinor Bose-Einstein condensates, partial trace, reduced density matrix, mean-field and Gross-Pitaevskii scaling, cubic NLS, coupled non-linear Schrödinger system.