Multiparameter estimation via an ensemble of spinor atoms
Min Zhuang, Jiahao Huang, Chaohong Lee · Physical Review A · 2018
Multiparameter estimation, which aims to simultaneously determine multiple parameters in the same measurement procedure, attracts extensive interest in measurement science and technologies. Here, we propose a multimode many-body quantum interferometry for simultaneously estimating linear and quadratic Zeeman coefficients via an ensemble of spinor atoms. Different from the scheme with individual atoms, by using a $N$-atom multimode Greenberger-Horne-Zeilinger state, the measurement precisions of the two parameters can simultaneously attain the Heisenberg scaling, and they respectively depend on the hyperfine spin number $F$ in the forms of $\mathrm{\ensuremath{\Delta}}p\ensuremath{\propto}1/(FN)$ and $\mathrm{\ensuremath{\Delta}}q\ensuremath{\propto}1/({F}^{2}N)$. Moreover, the simultaneous estimation can provide better precision than the individual estimation. Further, by taking a three-mode interferometry with Bose-condensed spin-1 atoms for an example, we show how to perform the simultaneous estimation of $p$ and $q$. Our scheme provides a novel paradigm for implementing multiparameter estimation with multimode quantum-correlated states.