Quantum-limited metrology in the presence of collisional dephasing

Abstract

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 ${\hat{J}}_x$, 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 $\propto 1/N^{3/2}$ for particle number $N$ and the dephasing rate $1<<\gamma <N^{3/4}$. With a ${\hat{J}}_y$ measurement, our analytical results confirm that the phase $\varphi =\chi t\sim 0$ can be detected at the limit even in the presence of the dephasing.

arXiv comment3.2 pages, 3 figures

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