Can a Quantum Nondemolition Measurement Improve the Sensitivity of an Atomic Magnetometer?

Abstract

We consider the limitations due to noise (e.g., quantum projection noise and photon shot-noise) on the sensitivity of an idealized atomic magnetometer that utilizes spin squeezing induced by a continuous quantum nondemolition measurement. Such a magnetometer measures spin precession of $N$ atomic spins by detecting optical rotation of far-detuned light. We show that for very short measurement times, the optimal sensitivity scales as $N^{-3/4}$; if strongly squeezed probe light is used, the Heisenberg limit of $N^{-1}$ scaling can be achieved. However, if the measurement time exceeds ${\tau }_{\mathrm{r}\mathrm{e}\mathrm{l}}/N^{1/2}$ in the former case, or ${\tau }_{\mathrm{r}\mathrm{e}\mathrm{l}}/N$ in the latter, where ${\tau }_{\mathrm{r}\mathrm{e}\mathrm{l}}$ is the spin relaxation time, the scaling becomes $N^{-1/2}$, as for a standard shot-noise-limited magnetometer.