Can a quantum nondemolition measurement improve the sensitivity of an atomic magnetometer?

Abstract

Noise properties of an idealized atomic magnetometer that utilizes spin squeezing induced by a continuous quantum nondemolition measurement are considered. Such a magnetometer measures spin precession of $N$ atomic spins by detecting optical rotation of far-detuned light. Fundamental noise sources include the quantum projection noise and the photon shot-noise. For measurement times much shorter than the spin-relaxation time divided by $\sqrt{N}$, the optimal sensitivity of the magnetometer scales as $N^{-3/4}$, so an advantage over the usual sensitivity scaling as $N^{-1/2}$ can be achieved, as demonstrated in a recent experiment by J. M. Geremia \emph{et al.} (quant-ph/0401107). However, at longer measurement times, the optimized sensitivity scales as $N^{-1/2}$, similarly to the usual shot-noise limited magnetometers. If strongly squeezed probe light is used, the Heisenberg uncertainty limit may, in principle, be reached for very short measurement times. However, if the exceedingly stringent limit (the spin-relaxation time divided by $N$) on the measurement time is exceeded, the $N^{-1/2}$ sensitivity is again restored.