Phase diffusion of a two-component Bose-Einstein condensates: exact and short-time solutions for arbitrary coherent spin state

We investigate phase diffusion of a two-component Bose-Einstein condensates prepared initially in arbitrary coherent spin state $\mathrm{\mid }{\theta }_0,{\varphi }_0⟩$. Analytical expression of the phase-diffusion time is presented for ${\theta }_0\mathrm{\ne }\pi \mathrm{/}2$ case. In comparison with the symmetrical case (i.e., ${\theta }_0=\pi \mathrm{/}2$), we find that the diffusion process becomes slowly due to the reduced atom number variance.