Quantum-limited metrology in the presence of collisional dephasing
Yong‐Chun Liu, Guangri Jin, Li You · Physical Review A · 2010
Including collisional decoherence explicitly, phase sensitivity for estimating effective scattering strength $\ensuremath{\chi}$ of a two-component Bose-Einstein condensate is derived analytically. With a measurement of spin operator ${\mathrm{J\ifmmode \hat{}\else \^{}\fi{}}}_{x}$, we find that the optimal sensitivity depends on initial coherent spin state. It degrades by a factor of $(2\ensuremath{\gamma}){}^{1/3}$ below super-Heisenberg limit $\ensuremath{\propto}1/{N}^{3/2}$ for particle number $N$ and the dephasing rate $1\ensuremath{\ll}\ensuremath{\gamma}<{N}^{3/4}$. With a ${\mathrm{J\ifmmode \hat{}\else \^{}\fi{}}}_{y}$ measurement, our analytical results confirm that the phase $\ensuremath{\phi}=\ensuremath{\chi}t~0$ can be detected at the limit even in the presence of the dephasing.