Quantum-limited metrology in the presence of collisional dephasing

Including collisional decoherence explicitly, phase sensitivity for estimating effective scattering strength chi of a two-component Bose-Einstein condensate is derived analytically. With a measurement of spin operator (J) over cap (x), we find that the optimal sensitivity depends on initial coherent spin state. It degrades by a factor of (2 gamma)(1/3) below super-Heisenberg limit alpha 1/N-3/2 for particle number N and the dephasing rate 1 << gamma < N-3/4. With a <(J)over cap>(y) measurement, our analytical results confirm that the phase phi = chi t similar to 0 can be detected at the limit even in the presence of the dephasing.