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 $|\theta_0,\phi_0\rangle$. Analytical expression of the phase-diffusion time is presented for $\theta_0\neq\pi/2$ case. In comparison with the symmetrical case (i.e., $\theta_0=\pi/2$), we find that the diffusion process becomes slowly due to the reduced atom number variance.