Magnetometry via a double-pass continuous quantum measurement of atomic spin

Bradley A. Chase, Heather L. Partner, Brigette D. Black, Benjamin Q. Baragiola and JM Geremia
Department of Physics and Astronomy, The University of New Mexico, Albuquerque NM 87131 USA

Abstract. We argue that it is possible in principle to reduce the uncertainty of an atomic magnetometer by double-passing a far-detuned laser field through the atomic sample as it undergoes Larmor precession. Numerical simulations of the quantum Fisher information suggest that, despite the lack of explicit multi-body coupling terms in the system's magnetic Hamiltonian, the parameter estimation uncertainty in such a physical setup scales better than the conventional Heisenberg uncertainty limit over a specified but arbitrary range of particle number N. Using the methods of quantum stochastic calculus and filtering theory, we demonstrate numerically an explicit parameter estimator (called a quantum particle filter) whose observed scaling follows that of our calculated quantum Fisher information. Moreover, the quantum particle filter quantitatively surpasses the uncertainty limit calculated from the quantum Cramer-Rao inequality based on a magnetic coupling Hamiltonian with only single-body operators. We also show that a quantum Kalman filter is insufficient to obtain super-Heisenberg scaling, and present evidence that such scaling necessitates going beyond the manifold of Gaussian atomic states.

Funded by: NSF (PHY-0639994); AFOSR (FA9550-06-01-0178)

Downloads

Please follow these links to download the available items in tar-gzip archive format. The laTeX source files include the draft document history, journal correspondence, and raw figure/graphics files. A compete archive of C++, mex and Matlab code used to implement the various filters described in the paper is also provided.

• [LaTeX Source and Figure Files] (tar.gz file with RevTeX source and pdf and eps figure files)
• [Simulation Code and Data Files] (tar.gz file with Matlab, mex and C++ source, including pre-compiled mex libraries for 32-bit windows, 64-bit windows, Intel Mac and PowerPC Mac architectures)

We have also provided access to some of the notes we generated during this research project, to provide a glimpse into the project as it progressed. The following archive includes derivations in the form of Mathematica notebooks and laTeX files describing those derivations.

• [Project Notes and Derivations] (tar.gz file containing laTeX source and .nb notebooks)

DISCLAIMER: these notes catalog the path we took toward the results presented in the paper, and therefore also include the history of mistakes and corrections that occurred in the research project. The notes are likely to include typographical errors and mistakes. Please keep that in mind when reading them.