In Situ Study of the Magnetic Field Gradient Produced by a Miniature Bi-Planar Coil for Chip-Scale Atomic Devices

doi:10.3390/mi14111985

. 2023 Oct 26;14(11):1985.

doi: 10.3390/mi14111985.

In Situ Study of the Magnetic Field Gradient Produced by a Miniature Bi-Planar Coil for Chip-Scale Atomic Devices

Yao Chen^{1

2}, Jiyang Wang¹, Ning Zhang³, Jing Wang⁴, Yintao Ma¹, Mingzhi Yu¹, Yanbin Wang¹, Libo Zhao¹, Zhuangde Jiang¹

Affiliations

¹ State Key Laboratory for Manufacturing Systems Engineering, International Joint Laboratory for Micro/Nano Manufacturing and Measurement Technologies, Overseas Expertise Introduction Center for Micro/Nano Manufacturing and Nano Measurement Technologies Discipline Innovation, School of Mechanical Engineering, Xi'an Jiaotong University, Xi'an 710049, China.
² Xi'an Jiaotong University Suzhou Institute, Suzhou 215123, China.
³ Research Center for Quantum Sensing, Intelligent Perception Research Institute, Zhejiang Lab, Hangzhou 311100, China.
⁴ Beijing Institute of Electronic System Engineering, Beijing 100854, China.

PMID: 38004842
PMCID: PMC10673043
DOI: 10.3390/mi14111985

In Situ Study of the Magnetic Field Gradient Produced by a Miniature Bi-Planar Coil for Chip-Scale Atomic Devices

Yao Chen et al. Micromachines (Basel). 2023.

. 2023 Oct 26;14(11):1985.

doi: 10.3390/mi14111985.

Authors

Yao Chen^{1

2}, Jiyang Wang¹, Ning Zhang³, Jing Wang⁴, Yintao Ma¹, Mingzhi Yu¹, Yanbin Wang¹, Libo Zhao¹, Zhuangde Jiang¹

Affiliations

¹ State Key Laboratory for Manufacturing Systems Engineering, International Joint Laboratory for Micro/Nano Manufacturing and Measurement Technologies, Overseas Expertise Introduction Center for Micro/Nano Manufacturing and Nano Measurement Technologies Discipline Innovation, School of Mechanical Engineering, Xi'an Jiaotong University, Xi'an 710049, China.
² Xi'an Jiaotong University Suzhou Institute, Suzhou 215123, China.
³ Research Center for Quantum Sensing, Intelligent Perception Research Institute, Zhejiang Lab, Hangzhou 311100, China.
⁴ Beijing Institute of Electronic System Engineering, Beijing 100854, China.

PMID: 38004842
PMCID: PMC10673043
DOI: 10.3390/mi14111985

Abstract

The miniaturization of quantum sensors is a popular trend for the development of quantum technology. One of the key components of these sensors is a coil which is used for spin modulation and manipulation. The bi-planar coils have the advantage of producing three-dimensional magnetic fields with only two planes of current confinement, whereas the traditional Helmholtz coils require three-dimensional current distribution. Thus, the bi-planar coils are compatible with the current micro-fabrication process and are quite suitable for the compact design of the chip-scale atomic devices that require stable or modulated magnetic fields. This paper presents a design of a miniature bi-planar coil. Both the magnetic fields produced by the coils and their inhomogeneities were designed theoretically. The magnetic field gradient is a crucial parameter for the coils, especially for generating magnetic fields in very small areas. We used a NMR (Nuclear Magnetic Resonance) method based on the relaxation of 131Xe nuclear spins to measure the magnetic field gradient in situ. This is the first time that the field inhomogeneities of the field of such small bi-planar coils have been measured. Our results indicate that the designed gradient caused error is 0.08 for the By and the Bx coils, and the measured gradient caused error using the nuclear spin relaxation method is 0.09±0.02, suggesting that our method is suitable for measuring gradients. Due to the poor sensitivity of our magnetometer under a large Bz bias field, we could not measure the Bz magnetic field gradient. Our method also helps to improve the gradients of the miniature bi-planar coil design, which is critical for chip-scale atomic devices.

Keywords: atomic magnetometer; chip-scale quantum sensors; magnetic field gradient; miniature bi-planar coil; optical pumped magnetometer.

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Conflict of interest statement

The authors declare no conflict of interest.

Figures

**Figure 2**
The figure displays the design of the bi-planar coil for the z direction, where the red lines represent the same direction of current flow.

**Figure 3**
The PCB drawing of $B_{x}$ , $B_{y}$ and $B_{z}$

**Figure 4**
The experimental setup for testing the bi-planar coil. PD: photo diode, NDF: neutral density filter, PBS: polarization beam splitter, GT: Glan–Taylor prism, PEEK: polyether ether ketone, PM: polarization maintaining. The bi-planar coils are set in the $x y$ plane. The two planes of the bi-planar coils are in parallel. The three pair bi-planar coils can produce three dimension magnetic fields. The $c o s (θ)$ coils are in a cylinder shape. The cylinder axial direction is the same as the heating laser beam direction. The $c o s (θ)$ coils [39] are arranged in such a way that they can produce z and y direction homogeneous magnetic fields. The cylinder also configures a Lee-Whiting coil, which could produce an x direction homogeneous magnetic field [40].

**Figure 5**
Typical Free Induction Decay (FID) signal of $^{131}$ Xe nuclear spins under a holding magnetic field produced by the bi-planar coil $B_{y}$ .

**Figure 6**
The relationship between the current in the bi-planar coil and the magnetic field strength measured by the precession frequency of $^{131}$ Xe nuclear spins for the x or y direction.

**Figure 7**
The FID signal of the $^{131}$ Xe nuclear spins under a y direction bigger coil ( $c o s (θ)$ coil) system with more uniform magnetic field gradients. The nuclear quadrupolar interaction induced beating signals can be resolved. The relaxation of the nuclear spins is smaller.

**Figure 8**
The FID signal of the $^{131}$ Xe nuclear spins under a bigger coil system with more uniform magnetic field gradients. The magnetic field was in the z direction. The relaxation rate was 0.30 $s^{- 1}$ .

**Figure 9**
The FID signal of the $^{131}$ Xe nuclear spins under the z bi-planar coil. The relaxation rate was 0.50 $s^{- 1}$ .

**Figure 10**
The magnetic field gradient produced by the y direction bi-planar coils. Due to symmetry, the x direction field gradient is similar. The color represents the error of the magnetic field, which is defined in Equation (2).

**Figure 11**
The magnetic field gradient produced by the z direction bi-planar coil.

**Figure 12**
The more detailed plotting of the magnetic field gradient produced by the y direction bi-planar coil. ‘y gradient’ represents $\partial B_{y} / \partial y$ and ‘z or x gradient’ represents ‘ $\partial B_{z} / \partial z$ or $\partial B_{x} / \partial x$ in the figure. Due to symmetry, the x direction bi-planar coil is similar.

**Figure 13**
The more detailed plotting of the magnetic field gradient produced by the z direction bi-planar coil. ‘z gradient’ represents $\partial B_{z} / \partial z$ and ‘x or y gradient’ represents $\partial B_{x} / \partial x$ or $\partial B_{y} / \partial y$ in the figure.

**Figure 14**
The relation between the magnetic field and the relaxation rate for the y bi-planar coil. Here, we did not directly measure the relationship between the magnetic field gradient and the relaxation rates. However, we directly measured the relationship between the magnetic field and relaxation rate because the magnetic field gradient can be calculated to be $ϵ_{a v g} B / 0.2$ cm in our design. The x bi-planar coil is similar.

See this image and copyright information in PMC

References

1. Kitching J. Chip-scale atomic devices. Appl. Phys. Rev. 2018;5:031302. doi: 10.1063/1.5026238. - DOI
1. Chen Y., Zhao L., Zhang N., Yu M., Ma Y., Han X., Zhao M., Lin Q., Yang P., Jiang Z. Single beam Cs-Ne SERF atomic magnetometer with the laser power differential method. Opt. Express. 2022;30:16541–16552. doi: 10.1364/OE.450571. - DOI - PubMed
1. Hunter D., Piccolomo S., Pritchard J.D., Brockie N.L., Dyer T.E., Riis E. Free-Induction-Decay Magnetometer Based on a Microfabricated Cs Vapor Cell. Phys. Rev. Appl. 2018;10:014002. doi: 10.1103/PhysRevApplied.10.014002. - DOI
1. Osborne J., Orton J., Alem O., Shah V. Fully integrated standalone zero field optically pumped magnetometer for biomagnetism; Proceedings of the Steep Dispersion Engineering and Opto-Atomic Precision Metrology XI. International Society for Optics and Photonics; San Francisco, CA, USA. 27 January–1 February 2018; pp. 89–95.
1. Krzyzewski S., Perry A., Gerginov V., Knappe S. Characterization of noise sources in a microfabricated single-beam zero-field optically-pumped magnetometer. Biomed. Opt. Express. 2019;126:044504. doi: 10.1063/1.5098088. - DOI - PMC - PubMed

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[1] Kitching J. Chip-scale atomic devices. Appl. Phys. Rev. 2018;5:031302. doi: 10.1063/1.5026238. - DOI

[2] Kitching J. Chip-scale atomic devices. Appl. Phys. Rev. 2018;5:031302. doi: 10.1063/1.5026238. - DOI

[3] Chen Y., Zhao L., Zhang N., Yu M., Ma Y., Han X., Zhao M., Lin Q., Yang P., Jiang Z. Single beam Cs-Ne SERF atomic magnetometer with the laser power differential method. Opt. Express. 2022;30:16541–16552. doi: 10.1364/OE.450571. - DOI - PubMed

[4] Chen Y., Zhao L., Zhang N., Yu M., Ma Y., Han X., Zhao M., Lin Q., Yang P., Jiang Z. Single beam Cs-Ne SERF atomic magnetometer with the laser power differential method. Opt. Express. 2022;30:16541–16552. doi: 10.1364/OE.450571. - DOI - PubMed

[5] Hunter D., Piccolomo S., Pritchard J.D., Brockie N.L., Dyer T.E., Riis E. Free-Induction-Decay Magnetometer Based on a Microfabricated Cs Vapor Cell. Phys. Rev. Appl. 2018;10:014002. doi: 10.1103/PhysRevApplied.10.014002. - DOI

[6] Hunter D., Piccolomo S., Pritchard J.D., Brockie N.L., Dyer T.E., Riis E. Free-Induction-Decay Magnetometer Based on a Microfabricated Cs Vapor Cell. Phys. Rev. Appl. 2018;10:014002. doi: 10.1103/PhysRevApplied.10.014002. - DOI

[7] Osborne J., Orton J., Alem O., Shah V. Fully integrated standalone zero field optically pumped magnetometer for biomagnetism; Proceedings of the Steep Dispersion Engineering and Opto-Atomic Precision Metrology XI. International Society for Optics and Photonics; San Francisco, CA, USA. 27 January–1 February 2018; pp. 89–95.

[8] Osborne J., Orton J., Alem O., Shah V. Fully integrated standalone zero field optically pumped magnetometer for biomagnetism; Proceedings of the Steep Dispersion Engineering and Opto-Atomic Precision Metrology XI. International Society for Optics and Photonics; San Francisco, CA, USA. 27 January–1 February 2018; pp. 89–95.

[9] Krzyzewski S., Perry A., Gerginov V., Knappe S. Characterization of noise sources in a microfabricated single-beam zero-field optically-pumped magnetometer. Biomed. Opt. Express. 2019;126:044504. doi: 10.1063/1.5098088. - DOI - PMC - PubMed

[10] Krzyzewski S., Perry A., Gerginov V., Knappe S. Characterization of noise sources in a microfabricated single-beam zero-field optically-pumped magnetometer. Biomed. Opt. Express. 2019;126:044504. doi: 10.1063/1.5098088. - DOI - PMC - PubMed

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In Situ Study of the Magnetic Field Gradient Produced by a Miniature Bi-Planar Coil for Chip-Scale Atomic Devices

Affiliations

In Situ Study of the Magnetic Field Gradient Produced by a Miniature Bi-Planar Coil for Chip-Scale Atomic Devices

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Affiliations

Abstract

Conflict of interest statement

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Abstract

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