Single-mode approximation in a spinor-1 atomic condensate

We investigate the validity conditions of the single-mode approximation (SMA) in a spinor-1 atomic condensate when effects due to residual magnetic fields are negligible. For atomic interactions of the ferromagnetic type, the SMA is shown to be exact, with a mode function different from what is commonly used. However, the quantitative deviation is small under current experimental conditions (for ⁸⁷Rb atoms). For antiferromagnetic interactions, we find that the SMA becomes invalid in general. The differences among the mean-field mode functions for the three spin components are shown to depend strongly on the system magnetization. Our results can be important for studies of beyond mean-field quantum correlations, such as fragmentation, spin squeezing, and multipartite entanglement.