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Phys Rev Lett. 2003 Dec 19;91(25):250801. Epub 2003 Dec 19.

Quantum Kalman filtering and the Heisenberg limit in atomic magnetometry.

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1
Norman Bridge Laboratory of Physics, California Institute of Technology, Pasadena, California, 91125, USA. jgeremia@Caltech.edu

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.

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