Quantum Kalman Filtering and the Heisenberg Limit in Atomic Magnetometry

The shot-noise detection limit in current high-precision atomic magnetometry is a manifestation of quantum fluctuations that scale as $1/\sqrt{N}$ in an ensemble of $N$ particles. However, there is a general expectation that the reduced projection noise provided by conditional spin-squeezing could be exploited to surpass the conventional shot-noise limit. We show that continuous measurement coupled with quantum Kalman filtering provides an optimal procedure for magnetic detection limits that scale with 1/N, the Heisenberg squeezing limit. Our analysis demonstrates the importance of optimal estimation procedures for high bandwidth precision magnetometry.