Reconstructing the profile of time-varying magnetic fields with quantum sensors
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magesan-2013-Reconstructing the profile.pdf
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Author(s)
Magesan, Easwar
Yum, Honam
Cappellaro, Paola
Cooper-Roy, Alexandre
Date Issued
September 2013
Journal
Physical Review A
Publisher
American Physical Society
Citation
Magesan, Easwar, Alexandre Cooper, Honam Yum, and Paola Cappellaro. “Reconstructing the profile of time-varying magnetic fields with quantum sensors.” Physical Review A 88, no. 3 (September 2013). © 2013 American Physical Society
Version
Final published version
Abstract
Quantum systems have shown great promise for precision metrology thanks to advances in their control. This has allowed not only the sensitive estimation of external parameters but also the reconstruction of their temporal profile. In particular, quantum control techniques and orthogonal function theory have been applied to the reconstruction of the complete profiles of time-varying magnetic fields. Here, we provide a detailed theoretical analysis of the reconstruction method based on the Walsh functions, highlighting the relationship between the orthonormal Walsh basis, sensitivity of field reconstructions, data compression techniques, and dynamical decoupling theory. Specifically, we show how properties of the Walsh basis and a detailed sensitivity analysis of the reconstruction protocol provide a method to characterize the error between the reconstructed and true fields. In addition, we prove various results about the negligibility function on binary sequences which lead to data compression techniques in the Walsh basis and a more resource-efficient reconstruction protocol. The negligibility proves a fruitful concept to unify the information content of Walsh functions and their dynamical decoupling power, which makes the reconstruction method robust against noise.
MIT Department
Massachusetts Institute of Technology. Department of Nuclear Science and Engineering
Massachusetts Institute of Technology. Research Laboratory of Electronics
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Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use.
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DOI of Published Version
https://doi.org/10.1103/PhysRevA.88.032107
