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 |θ₀, varphi₀). Analytical expression of the phase-diffusion time is presented for θ₀ ≠ π/2 case. In comparison with the symmetrical case (i.e., θ₀ = π/2), we find that the diffusion process becomes slow due to the reduced atom number variance.