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Fitting magnetic field gradient with Heisenberg-scaling accuracy.

Zhang YL, Wang H, Jing L, Mu LZ, Fan H - Sci Rep (2014)

Bottom Line: Our scheme combines the quantum multi-parameter estimation and the least square linear fitting method to achieve the quantum Cramér-Rao bound (QCRB).We show that the estimated quantity achieves the Heisenberg-scaling accuracy.Our scheme of quantum metrology combined with data fitting provides a new method in fast high precision measurements.

View Article: PubMed Central - PubMed

Affiliation: School of Physics, Peking University, Beijing 100871, China.

ABSTRACT
The linear function is possibly the simplest and the most used relation appearing in various areas of our world. A linear relation can be generally determined by the least square linear fitting (LSLF) method using several measured quantities depending on variables. This happens for such as detecting the gradient of a magnetic field. Here, we propose a quantum fitting scheme to estimate the magnetic field gradient with N-atom spins preparing in W state. Our scheme combines the quantum multi-parameter estimation and the least square linear fitting method to achieve the quantum Cramér-Rao bound (QCRB). We show that the estimated quantity achieves the Heisenberg-scaling accuracy. Our scheme of quantum metrology combined with data fitting provides a new method in fast high precision measurements.

No MeSH data available.


The schematic of the system.The atomic spin chain is coupled to a magnetic field, where each atom is separated with a distance a in the x-direction.
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f1: The schematic of the system.The atomic spin chain is coupled to a magnetic field, where each atom is separated with a distance a in the x-direction.

Mentions: We consider the problem of measuring the gradient of a magnetic field. Our scheme is to simultaneously estimate the strength of magnetic field at different locations through quantum measurements and then to apply the LSLF method. We employ a N-atom spin chain as the probes, as shown in FIG. 1, to estimate the magnetic field gradient, where the j-th atom is located at xj = x1 + (j − 1)a, () and the uncertainty of the location xj can be neglected. The Hamiltonian describes that each atom with two hyperfine spin states is coupled to the local magnetic field, and it takes the form, where Bj and are the magnetic field and Pauli operator of atom j, and each atom has the same gyromagnetic ratio γ. The task of our scheme is to obtain optimal uncertainty bound of estimating the magnetic field gradient G that quantum mechanics permitted.


Fitting magnetic field gradient with Heisenberg-scaling accuracy.

Zhang YL, Wang H, Jing L, Mu LZ, Fan H - Sci Rep (2014)

The schematic of the system.The atomic spin chain is coupled to a magnetic field, where each atom is separated with a distance a in the x-direction.
© Copyright Policy - open-access
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC4260217&req=5

f1: The schematic of the system.The atomic spin chain is coupled to a magnetic field, where each atom is separated with a distance a in the x-direction.
Mentions: We consider the problem of measuring the gradient of a magnetic field. Our scheme is to simultaneously estimate the strength of magnetic field at different locations through quantum measurements and then to apply the LSLF method. We employ a N-atom spin chain as the probes, as shown in FIG. 1, to estimate the magnetic field gradient, where the j-th atom is located at xj = x1 + (j − 1)a, () and the uncertainty of the location xj can be neglected. The Hamiltonian describes that each atom with two hyperfine spin states is coupled to the local magnetic field, and it takes the form, where Bj and are the magnetic field and Pauli operator of atom j, and each atom has the same gyromagnetic ratio γ. The task of our scheme is to obtain optimal uncertainty bound of estimating the magnetic field gradient G that quantum mechanics permitted.

Bottom Line: Our scheme combines the quantum multi-parameter estimation and the least square linear fitting method to achieve the quantum Cramér-Rao bound (QCRB).We show that the estimated quantity achieves the Heisenberg-scaling accuracy.Our scheme of quantum metrology combined with data fitting provides a new method in fast high precision measurements.

View Article: PubMed Central - PubMed

Affiliation: School of Physics, Peking University, Beijing 100871, China.

ABSTRACT
The linear function is possibly the simplest and the most used relation appearing in various areas of our world. A linear relation can be generally determined by the least square linear fitting (LSLF) method using several measured quantities depending on variables. This happens for such as detecting the gradient of a magnetic field. Here, we propose a quantum fitting scheme to estimate the magnetic field gradient with N-atom spins preparing in W state. Our scheme combines the quantum multi-parameter estimation and the least square linear fitting method to achieve the quantum Cramér-Rao bound (QCRB). We show that the estimated quantity achieves the Heisenberg-scaling accuracy. Our scheme of quantum metrology combined with data fitting provides a new method in fast high precision measurements.

No MeSH data available.