A femtotesla pulsed gradiometer using multipass cells at finite fields

We describe a $^{\mathrm{\thinspace 87}}$Rb scalar gradiometer using two multipass cells which increase the path length of the probe beam by one order of magnitude. This gives a much higher optical depth on resonance, which is crucial for quantum-nondemolition (QND) measurements. As a result, we can directly record a large optical rotation. When the optical rotation exceeds $\pi $/4 radians, the optical rotation signal wraps around, showing multiple zero-crossings in a single Larmor period. This exotic signal gains a higher signal intensity, which indicates that a single photon can interact with higher number of alkali atoms. The magnetic field sensitivity then can reach beyond the naive Cramer-Rao lower bound, the minimum bound for the estimated frequency variance of a sine wave in the presence of photon shot noise. The lower probe power consumption is also critical for development of a miniaturized magnetometer. We have implemented a novel method of zero-crossing detection of the wrapped signals. We report a magnetic sensitivity of 7 fT/$\surd $Hz in the geomagnetic field range, which agrees well with the quantum spin noise limit.