Quantum-limited metrology in the presence of collisional dephasing

TL;DR

This paper analytically investigates the impact of collisional dephasing on phase sensitivity in quantum metrology with Bose-Einstein condensates, revealing how decoherence degrades measurement precision and identifying optimal measurement strategies.

Contribution

It provides an analytical framework for understanding how collisional dephasing affects quantum metrology sensitivity in BECs, including optimal measurement choices and sensitivity limits.

Findings

Sensitivity degrades by a factor of (2γ)^{1/3} below super-Heisenberg limit

J_x measurement sensitivity depends on initial spin state

J_y measurement can detect phase at the limit despite 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 $\phi=\chi t\sim 0$ can be detected at the limit even in the presence of the dephasing.