title: Quantum Kalman filtering and the Heisenberg limit in atomic magnetometry.
abstract: The shot-noise detection limit in current high-precision magnetometry [Nature (London) 422, 596 (2003)] is a manifestation of quantum fluctuations that scale as 1/sqrt[N] in an ensemble of N atoms. Here, we develop a procedure that combines continuous measurement and quantum Kalman filtering [Rep. Math. Phys. 43, 405 (1999)]] to surpass this conventional limit by exploiting conditional spin squeezing to achieve 1/N field sensitivity. Our analysis demonstrates the importance of optimal estimation for high bandwidth precision magnetometry at the Heisenberg limit and also identifies an approximate estimator based on linear regression.
authors.affiliation: Norman Bridge Laboratory of Physics, California Institute of Technology, Pasadena, California, 91125, USA. jgeremia@Caltech.edu
authors.forename: J M
authors.initials: JM
authors.lastname: Geremia
authors.forename: John K
authors.initials: JK
authors.lastname: Stockton
authors.forename: Andrew C
authors.initials: AC
authors.lastname: Doherty
authors.forename: Hideo
authors.initials: H
authors.lastname: Mabuchi