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{sub x}, we find that the optimal sensitivity depends on initial coherent spin state. It degrades by a factor of (2{gamma}){sup 1/3} below super-Heisenberg limit {proportional_to}1/N{sup 3/2} for particle number N and the dephasing rate 1<<{gamma}<N{sup 3/4}. With a J{sub y} measurement, our analytical results confirm that the phase {phi}={chi}t{approx}0 can be detected at the limit even in the presence of the dephasing.