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Zeptonewton and Attotesla per Centimeter Metrology With Coupled Oscillators

Published 22 Feb 2024 in physics.app-ph | (2402.14678v2)

Abstract: We present the coupled oscillator: a new mechanism for signal amplification with widespread application in metrology. We introduce the mechanical theory of this framework, and support it by way of simulations. We present a particular implementation of coupled oscillators: a microelectromechanical system (MEMS) that uses one large (~100mm) N52 magnet coupled magnetically to a small (~0.25mm), oscillating N52 magnet, providing a force resolution of 200zN measured over 1s in a noiseless environment. We show that the same system is able to resolve magnetic gradients of 130aT/cm at a single point (within 500um). This technology therefore has the potential to revolutionize force and magnetic gradient sensing, including high-impact areas such cardiac and brain imaging.

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References (17)
  1. Javor, J. et al. Zeptometer Metrology Using the Casimir Effect, Journal of Low Temperature Physics 208:147–159 (2022) [4] Imboden, M. et al. Design of a Casimir-driven parametric amplifier. Journal of Applied (2014); 116 (13): 134504 [5] Zhang, X., et al. Precision measurement and frequency metrology with ultracold atoms, National Science Review 3:189–200 (2016) [6] Chang, L. Foundations of MEMS (Second Edition), Pearson Education Asia (2012) [7] Asztalos, S. J. et al. A SQUID-based microwave cavity search for dark-matter axions, Physical Review Letters, 104 (4) (2010) [8] K. D. Irwin et al. Transition-edge sensors, Cryogenic Particle Detection, Springer (2005) [9] East Asian Observatory SCUBA-2. https://www.eaobservatory.org/jcmt/instrumentation/continuum/scuba-2/ (2019) [Accessed May 17, 2024] [10] Yao, X. et al. Background noise estimation of the geomagnetic signal, Geosci. Instrum. Method. Data Syst., 7, 189–193 (2018) [11] Swain, P. P. et al. A feasibility study to measure magnetocardiography (MCG) in unshielded environment using first order gradiometer, Biomed. Signal Process. Control 55, 101664 (2020) [12] Hämäläinen, M., et al. Magnetoencephalography — theory, instrumentation, and applications to noninvasive studies of the working human brain, Reviews of Modern Physics, 65(2): 413–497 (1993) [13] Albrecht, T. R., et al. Frequency modulation detection using high‐Q cantilevers for enhanced force microscope sensitivity, Journal of Applied Physics 69(2): 668-673 (1991) [14] Nony, L., et al. A nc-AFM simulator with Phase Locked Loop-controlled frequency detection and excitation, arxiv preprint https://arxiv.org/abs/physics/0701343 (2007) [15] Stange et al. Building a Casimir metrology platform using a commercial MEMS sensor Microsystems & Nanoengineering (2019) [16] H. B. Chan, et. al. Quantum Mechanical Actuation of Microelectromechanical Systems by the Casimir Force, Science 291:1941-1944 (2001) [17] Advanced Magnets Co. Typical Physical and Chemical Properties of Some Magnetic Materials. https://www.advancedmagnets.com/custom-magnets/ (2022) [Accessed Jan. 29, 2024]. [18] Javor, J. et al. 100 pT/cm single-point MEMS magnetic gradiometer from a commercial accelerometer. Microsyst. Nanoeng. 6, 1–13 (2020) [19] Porr B, et. al. Real-time noise cancellation with deep learning, PLoS One (2022) Imboden, M. et al. Design of a Casimir-driven parametric amplifier. Journal of Applied (2014); 116 (13): 134504 [5] Zhang, X., et al. Precision measurement and frequency metrology with ultracold atoms, National Science Review 3:189–200 (2016) [6] Chang, L. Foundations of MEMS (Second Edition), Pearson Education Asia (2012) [7] Asztalos, S. J. et al. A SQUID-based microwave cavity search for dark-matter axions, Physical Review Letters, 104 (4) (2010) [8] K. D. Irwin et al. Transition-edge sensors, Cryogenic Particle Detection, Springer (2005) [9] East Asian Observatory SCUBA-2. https://www.eaobservatory.org/jcmt/instrumentation/continuum/scuba-2/ (2019) [Accessed May 17, 2024] [10] Yao, X. et al. Background noise estimation of the geomagnetic signal, Geosci. Instrum. Method. Data Syst., 7, 189–193 (2018) [11] Swain, P. P. et al. A feasibility study to measure magnetocardiography (MCG) in unshielded environment using first order gradiometer, Biomed. Signal Process. Control 55, 101664 (2020) [12] Hämäläinen, M., et al. Magnetoencephalography — theory, instrumentation, and applications to noninvasive studies of the working human brain, Reviews of Modern Physics, 65(2): 413–497 (1993) [13] Albrecht, T. R., et al. Frequency modulation detection using high‐Q cantilevers for enhanced force microscope sensitivity, Journal of Applied Physics 69(2): 668-673 (1991) [14] Nony, L., et al. A nc-AFM simulator with Phase Locked Loop-controlled frequency detection and excitation, arxiv preprint https://arxiv.org/abs/physics/0701343 (2007) [15] Stange et al. Building a Casimir metrology platform using a commercial MEMS sensor Microsystems & Nanoengineering (2019) [16] H. B. Chan, et. al. Quantum Mechanical Actuation of Microelectromechanical Systems by the Casimir Force, Science 291:1941-1944 (2001) [17] Advanced Magnets Co. Typical Physical and Chemical Properties of Some Magnetic Materials. https://www.advancedmagnets.com/custom-magnets/ (2022) [Accessed Jan. 29, 2024]. [18] Javor, J. et al. 100 pT/cm single-point MEMS magnetic gradiometer from a commercial accelerometer. Microsyst. Nanoeng. 6, 1–13 (2020) [19] Porr B, et. al. Real-time noise cancellation with deep learning, PLoS One (2022) Zhang, X., et al. Precision measurement and frequency metrology with ultracold atoms, National Science Review 3:189–200 (2016) [6] Chang, L. Foundations of MEMS (Second Edition), Pearson Education Asia (2012) [7] Asztalos, S. J. et al. A SQUID-based microwave cavity search for dark-matter axions, Physical Review Letters, 104 (4) (2010) [8] K. D. Irwin et al. Transition-edge sensors, Cryogenic Particle Detection, Springer (2005) [9] East Asian Observatory SCUBA-2. https://www.eaobservatory.org/jcmt/instrumentation/continuum/scuba-2/ (2019) [Accessed May 17, 2024] [10] Yao, X. et al. Background noise estimation of the geomagnetic signal, Geosci. Instrum. Method. Data Syst., 7, 189–193 (2018) [11] Swain, P. P. et al. A feasibility study to measure magnetocardiography (MCG) in unshielded environment using first order gradiometer, Biomed. Signal Process. Control 55, 101664 (2020) [12] Hämäläinen, M., et al. Magnetoencephalography — theory, instrumentation, and applications to noninvasive studies of the working human brain, Reviews of Modern Physics, 65(2): 413–497 (1993) [13] Albrecht, T. R., et al. Frequency modulation detection using high‐Q cantilevers for enhanced force microscope sensitivity, Journal of Applied Physics 69(2): 668-673 (1991) [14] Nony, L., et al. A nc-AFM simulator with Phase Locked Loop-controlled frequency detection and excitation, arxiv preprint https://arxiv.org/abs/physics/0701343 (2007) [15] Stange et al. Building a Casimir metrology platform using a commercial MEMS sensor Microsystems & Nanoengineering (2019) [16] H. B. Chan, et. al. Quantum Mechanical Actuation of Microelectromechanical Systems by the Casimir Force, Science 291:1941-1944 (2001) [17] Advanced Magnets Co. Typical Physical and Chemical Properties of Some Magnetic Materials. https://www.advancedmagnets.com/custom-magnets/ (2022) [Accessed Jan. 29, 2024]. [18] Javor, J. et al. 100 pT/cm single-point MEMS magnetic gradiometer from a commercial accelerometer. Microsyst. Nanoeng. 6, 1–13 (2020) [19] Porr B, et. al. Real-time noise cancellation with deep learning, PLoS One (2022) Chang, L. Foundations of MEMS (Second Edition), Pearson Education Asia (2012) [7] Asztalos, S. J. et al. A SQUID-based microwave cavity search for dark-matter axions, Physical Review Letters, 104 (4) (2010) [8] K. D. Irwin et al. Transition-edge sensors, Cryogenic Particle Detection, Springer (2005) [9] East Asian Observatory SCUBA-2. https://www.eaobservatory.org/jcmt/instrumentation/continuum/scuba-2/ (2019) [Accessed May 17, 2024] [10] Yao, X. et al. Background noise estimation of the geomagnetic signal, Geosci. Instrum. Method. Data Syst., 7, 189–193 (2018) [11] Swain, P. P. et al. A feasibility study to measure magnetocardiography (MCG) in unshielded environment using first order gradiometer, Biomed. Signal Process. Control 55, 101664 (2020) [12] Hämäläinen, M., et al. Magnetoencephalography — theory, instrumentation, and applications to noninvasive studies of the working human brain, Reviews of Modern Physics, 65(2): 413–497 (1993) [13] Albrecht, T. R., et al. Frequency modulation detection using high‐Q cantilevers for enhanced force microscope sensitivity, Journal of Applied Physics 69(2): 668-673 (1991) [14] Nony, L., et al. A nc-AFM simulator with Phase Locked Loop-controlled frequency detection and excitation, arxiv preprint https://arxiv.org/abs/physics/0701343 (2007) [15] Stange et al. Building a Casimir metrology platform using a commercial MEMS sensor Microsystems & Nanoengineering (2019) [16] H. B. Chan, et. al. Quantum Mechanical Actuation of Microelectromechanical Systems by the Casimir Force, Science 291:1941-1944 (2001) [17] Advanced Magnets Co. Typical Physical and Chemical Properties of Some Magnetic Materials. https://www.advancedmagnets.com/custom-magnets/ (2022) [Accessed Jan. 29, 2024]. [18] Javor, J. et al. 100 pT/cm single-point MEMS magnetic gradiometer from a commercial accelerometer. Microsyst. Nanoeng. 6, 1–13 (2020) [19] Porr B, et. al. Real-time noise cancellation with deep learning, PLoS One (2022) Asztalos, S. J. et al. A SQUID-based microwave cavity search for dark-matter axions, Physical Review Letters, 104 (4) (2010) [8] K. D. Irwin et al. Transition-edge sensors, Cryogenic Particle Detection, Springer (2005) [9] East Asian Observatory SCUBA-2. https://www.eaobservatory.org/jcmt/instrumentation/continuum/scuba-2/ (2019) [Accessed May 17, 2024] [10] Yao, X. et al. Background noise estimation of the geomagnetic signal, Geosci. Instrum. Method. Data Syst., 7, 189–193 (2018) [11] Swain, P. P. et al. A feasibility study to measure magnetocardiography (MCG) in unshielded environment using first order gradiometer, Biomed. Signal Process. Control 55, 101664 (2020) [12] Hämäläinen, M., et al. Magnetoencephalography — theory, instrumentation, and applications to noninvasive studies of the working human brain, Reviews of Modern Physics, 65(2): 413–497 (1993) [13] Albrecht, T. R., et al. Frequency modulation detection using high‐Q cantilevers for enhanced force microscope sensitivity, Journal of Applied Physics 69(2): 668-673 (1991) [14] Nony, L., et al. A nc-AFM simulator with Phase Locked Loop-controlled frequency detection and excitation, arxiv preprint https://arxiv.org/abs/physics/0701343 (2007) [15] Stange et al. Building a Casimir metrology platform using a commercial MEMS sensor Microsystems & Nanoengineering (2019) [16] H. B. Chan, et. al. Quantum Mechanical Actuation of Microelectromechanical Systems by the Casimir Force, Science 291:1941-1944 (2001) [17] Advanced Magnets Co. Typical Physical and Chemical Properties of Some Magnetic Materials. https://www.advancedmagnets.com/custom-magnets/ (2022) [Accessed Jan. 29, 2024]. [18] Javor, J. et al. 100 pT/cm single-point MEMS magnetic gradiometer from a commercial accelerometer. Microsyst. Nanoeng. 6, 1–13 (2020) [19] Porr B, et. al. Real-time noise cancellation with deep learning, PLoS One (2022) K. D. Irwin et al. Transition-edge sensors, Cryogenic Particle Detection, Springer (2005) [9] East Asian Observatory SCUBA-2. https://www.eaobservatory.org/jcmt/instrumentation/continuum/scuba-2/ (2019) [Accessed May 17, 2024] [10] Yao, X. et al. Background noise estimation of the geomagnetic signal, Geosci. Instrum. Method. Data Syst., 7, 189–193 (2018) [11] Swain, P. P. et al. A feasibility study to measure magnetocardiography (MCG) in unshielded environment using first order gradiometer, Biomed. Signal Process. Control 55, 101664 (2020) [12] Hämäläinen, M., et al. Magnetoencephalography — theory, instrumentation, and applications to noninvasive studies of the working human brain, Reviews of Modern Physics, 65(2): 413–497 (1993) [13] Albrecht, T. R., et al. Frequency modulation detection using high‐Q cantilevers for enhanced force microscope sensitivity, Journal of Applied Physics 69(2): 668-673 (1991) [14] Nony, L., et al. A nc-AFM simulator with Phase Locked Loop-controlled frequency detection and excitation, arxiv preprint https://arxiv.org/abs/physics/0701343 (2007) [15] Stange et al. Building a Casimir metrology platform using a commercial MEMS sensor Microsystems & Nanoengineering (2019) [16] H. B. Chan, et. al. Quantum Mechanical Actuation of Microelectromechanical Systems by the Casimir Force, Science 291:1941-1944 (2001) [17] Advanced Magnets Co. Typical Physical and Chemical Properties of Some Magnetic Materials. https://www.advancedmagnets.com/custom-magnets/ (2022) [Accessed Jan. 29, 2024]. [18] Javor, J. et al. 100 pT/cm single-point MEMS magnetic gradiometer from a commercial accelerometer. Microsyst. Nanoeng. 6, 1–13 (2020) [19] Porr B, et. al. Real-time noise cancellation with deep learning, PLoS One (2022) East Asian Observatory SCUBA-2. https://www.eaobservatory.org/jcmt/instrumentation/continuum/scuba-2/ (2019) [Accessed May 17, 2024] [10] Yao, X. et al. Background noise estimation of the geomagnetic signal, Geosci. Instrum. Method. Data Syst., 7, 189–193 (2018) [11] Swain, P. P. et al. A feasibility study to measure magnetocardiography (MCG) in unshielded environment using first order gradiometer, Biomed. Signal Process. Control 55, 101664 (2020) [12] Hämäläinen, M., et al. Magnetoencephalography — theory, instrumentation, and applications to noninvasive studies of the working human brain, Reviews of Modern Physics, 65(2): 413–497 (1993) [13] Albrecht, T. R., et al. Frequency modulation detection using high‐Q cantilevers for enhanced force microscope sensitivity, Journal of Applied Physics 69(2): 668-673 (1991) [14] Nony, L., et al. A nc-AFM simulator with Phase Locked Loop-controlled frequency detection and excitation, arxiv preprint https://arxiv.org/abs/physics/0701343 (2007) [15] Stange et al. Building a Casimir metrology platform using a commercial MEMS sensor Microsystems & Nanoengineering (2019) [16] H. B. Chan, et. al. Quantum Mechanical Actuation of Microelectromechanical Systems by the Casimir Force, Science 291:1941-1944 (2001) [17] Advanced Magnets Co. Typical Physical and Chemical Properties of Some Magnetic Materials. https://www.advancedmagnets.com/custom-magnets/ (2022) [Accessed Jan. 29, 2024]. [18] Javor, J. et al. 100 pT/cm single-point MEMS magnetic gradiometer from a commercial accelerometer. Microsyst. Nanoeng. 6, 1–13 (2020) [19] Porr B, et. al. Real-time noise cancellation with deep learning, PLoS One (2022) Yao, X. et al. Background noise estimation of the geomagnetic signal, Geosci. Instrum. Method. Data Syst., 7, 189–193 (2018) [11] Swain, P. P. et al. A feasibility study to measure magnetocardiography (MCG) in unshielded environment using first order gradiometer, Biomed. Signal Process. Control 55, 101664 (2020) [12] Hämäläinen, M., et al. Magnetoencephalography — theory, instrumentation, and applications to noninvasive studies of the working human brain, Reviews of Modern Physics, 65(2): 413–497 (1993) [13] Albrecht, T. R., et al. Frequency modulation detection using high‐Q cantilevers for enhanced force microscope sensitivity, Journal of Applied Physics 69(2): 668-673 (1991) [14] Nony, L., et al. A nc-AFM simulator with Phase Locked Loop-controlled frequency detection and excitation, arxiv preprint https://arxiv.org/abs/physics/0701343 (2007) [15] Stange et al. Building a Casimir metrology platform using a commercial MEMS sensor Microsystems & Nanoengineering (2019) [16] H. B. Chan, et. al. Quantum Mechanical Actuation of Microelectromechanical Systems by the Casimir Force, Science 291:1941-1944 (2001) [17] Advanced Magnets Co. Typical Physical and Chemical Properties of Some Magnetic Materials. https://www.advancedmagnets.com/custom-magnets/ (2022) [Accessed Jan. 29, 2024]. [18] Javor, J. et al. 100 pT/cm single-point MEMS magnetic gradiometer from a commercial accelerometer. Microsyst. Nanoeng. 6, 1–13 (2020) [19] Porr B, et. al. Real-time noise cancellation with deep learning, PLoS One (2022) Swain, P. P. et al. A feasibility study to measure magnetocardiography (MCG) in unshielded environment using first order gradiometer, Biomed. Signal Process. Control 55, 101664 (2020) [12] Hämäläinen, M., et al. Magnetoencephalography — theory, instrumentation, and applications to noninvasive studies of the working human brain, Reviews of Modern Physics, 65(2): 413–497 (1993) [13] Albrecht, T. R., et al. Frequency modulation detection using high‐Q cantilevers for enhanced force microscope sensitivity, Journal of Applied Physics 69(2): 668-673 (1991) [14] Nony, L., et al. A nc-AFM simulator with Phase Locked Loop-controlled frequency detection and excitation, arxiv preprint https://arxiv.org/abs/physics/0701343 (2007) [15] Stange et al. Building a Casimir metrology platform using a commercial MEMS sensor Microsystems & Nanoengineering (2019) [16] H. B. Chan, et. al. Quantum Mechanical Actuation of Microelectromechanical Systems by the Casimir Force, Science 291:1941-1944 (2001) [17] Advanced Magnets Co. Typical Physical and Chemical Properties of Some Magnetic Materials. https://www.advancedmagnets.com/custom-magnets/ (2022) [Accessed Jan. 29, 2024]. [18] Javor, J. et al. 100 pT/cm single-point MEMS magnetic gradiometer from a commercial accelerometer. Microsyst. Nanoeng. 6, 1–13 (2020) [19] Porr B, et. al. Real-time noise cancellation with deep learning, PLoS One (2022) Hämäläinen, M., et al. Magnetoencephalography — theory, instrumentation, and applications to noninvasive studies of the working human brain, Reviews of Modern Physics, 65(2): 413–497 (1993) [13] Albrecht, T. R., et al. Frequency modulation detection using high‐Q cantilevers for enhanced force microscope sensitivity, Journal of Applied Physics 69(2): 668-673 (1991) [14] Nony, L., et al. A nc-AFM simulator with Phase Locked Loop-controlled frequency detection and excitation, arxiv preprint https://arxiv.org/abs/physics/0701343 (2007) [15] Stange et al. Building a Casimir metrology platform using a commercial MEMS sensor Microsystems & Nanoengineering (2019) [16] H. B. Chan, et. al. Quantum Mechanical Actuation of Microelectromechanical Systems by the Casimir Force, Science 291:1941-1944 (2001) [17] Advanced Magnets Co. Typical Physical and Chemical Properties of Some Magnetic Materials. https://www.advancedmagnets.com/custom-magnets/ (2022) [Accessed Jan. 29, 2024]. [18] Javor, J. et al. 100 pT/cm single-point MEMS magnetic gradiometer from a commercial accelerometer. Microsyst. Nanoeng. 6, 1–13 (2020) [19] Porr B, et. al. Real-time noise cancellation with deep learning, PLoS One (2022) Albrecht, T. R., et al. Frequency modulation detection using high‐Q cantilevers for enhanced force microscope sensitivity, Journal of Applied Physics 69(2): 668-673 (1991) [14] Nony, L., et al. A nc-AFM simulator with Phase Locked Loop-controlled frequency detection and excitation, arxiv preprint https://arxiv.org/abs/physics/0701343 (2007) [15] Stange et al. Building a Casimir metrology platform using a commercial MEMS sensor Microsystems & Nanoengineering (2019) [16] H. B. Chan, et. al. Quantum Mechanical Actuation of Microelectromechanical Systems by the Casimir Force, Science 291:1941-1944 (2001) [17] Advanced Magnets Co. Typical Physical and Chemical Properties of Some Magnetic Materials. https://www.advancedmagnets.com/custom-magnets/ (2022) [Accessed Jan. 29, 2024]. [18] Javor, J. et al. 100 pT/cm single-point MEMS magnetic gradiometer from a commercial accelerometer. Microsyst. Nanoeng. 6, 1–13 (2020) [19] Porr B, et. al. Real-time noise cancellation with deep learning, PLoS One (2022) Nony, L., et al. A nc-AFM simulator with Phase Locked Loop-controlled frequency detection and excitation, arxiv preprint https://arxiv.org/abs/physics/0701343 (2007) [15] Stange et al. Building a Casimir metrology platform using a commercial MEMS sensor Microsystems & Nanoengineering (2019) [16] H. B. Chan, et. al. Quantum Mechanical Actuation of Microelectromechanical Systems by the Casimir Force, Science 291:1941-1944 (2001) [17] Advanced Magnets Co. Typical Physical and Chemical Properties of Some Magnetic Materials. https://www.advancedmagnets.com/custom-magnets/ (2022) [Accessed Jan. 29, 2024]. [18] Javor, J. et al. 100 pT/cm single-point MEMS magnetic gradiometer from a commercial accelerometer. Microsyst. Nanoeng. 6, 1–13 (2020) [19] Porr B, et. al. Real-time noise cancellation with deep learning, PLoS One (2022) Stange et al. Building a Casimir metrology platform using a commercial MEMS sensor Microsystems & Nanoengineering (2019) [16] H. B. Chan, et. al. Quantum Mechanical Actuation of Microelectromechanical Systems by the Casimir Force, Science 291:1941-1944 (2001) [17] Advanced Magnets Co. Typical Physical and Chemical Properties of Some Magnetic Materials. https://www.advancedmagnets.com/custom-magnets/ (2022) [Accessed Jan. 29, 2024]. [18] Javor, J. et al. 100 pT/cm single-point MEMS magnetic gradiometer from a commercial accelerometer. Microsyst. Nanoeng. 6, 1–13 (2020) [19] Porr B, et. al. Real-time noise cancellation with deep learning, PLoS One (2022) H. B. Chan, et. al. Quantum Mechanical Actuation of Microelectromechanical Systems by the Casimir Force, Science 291:1941-1944 (2001) [17] Advanced Magnets Co. Typical Physical and Chemical Properties of Some Magnetic Materials. https://www.advancedmagnets.com/custom-magnets/ (2022) [Accessed Jan. 29, 2024]. [18] Javor, J. et al. 100 pT/cm single-point MEMS magnetic gradiometer from a commercial accelerometer. Microsyst. Nanoeng. 6, 1–13 (2020) [19] Porr B, et. al. Real-time noise cancellation with deep learning, PLoS One (2022) Advanced Magnets Co. Typical Physical and Chemical Properties of Some Magnetic Materials. https://www.advancedmagnets.com/custom-magnets/ (2022) [Accessed Jan. 29, 2024]. [18] Javor, J. et al. 100 pT/cm single-point MEMS magnetic gradiometer from a commercial accelerometer. Microsyst. Nanoeng. 6, 1–13 (2020) [19] Porr B, et. al. Real-time noise cancellation with deep learning, PLoS One (2022) Javor, J. et al. 100 pT/cm single-point MEMS magnetic gradiometer from a commercial accelerometer. Microsyst. Nanoeng. 6, 1–13 (2020) [19] Porr B, et. al. Real-time noise cancellation with deep learning, PLoS One (2022) Porr B, et. al. Real-time noise cancellation with deep learning, PLoS One (2022)
  2. Imboden, M. et al. Design of a Casimir-driven parametric amplifier. Journal of Applied (2014); 116 (13): 134504 [5] Zhang, X., et al. Precision measurement and frequency metrology with ultracold atoms, National Science Review 3:189–200 (2016) [6] Chang, L. Foundations of MEMS (Second Edition), Pearson Education Asia (2012) [7] Asztalos, S. J. et al. A SQUID-based microwave cavity search for dark-matter axions, Physical Review Letters, 104 (4) (2010) [8] K. D. Irwin et al. Transition-edge sensors, Cryogenic Particle Detection, Springer (2005) [9] East Asian Observatory SCUBA-2. https://www.eaobservatory.org/jcmt/instrumentation/continuum/scuba-2/ (2019) [Accessed May 17, 2024] [10] Yao, X. et al. Background noise estimation of the geomagnetic signal, Geosci. Instrum. Method. Data Syst., 7, 189–193 (2018) [11] Swain, P. P. et al. A feasibility study to measure magnetocardiography (MCG) in unshielded environment using first order gradiometer, Biomed. Signal Process. Control 55, 101664 (2020) [12] Hämäläinen, M., et al. Magnetoencephalography — theory, instrumentation, and applications to noninvasive studies of the working human brain, Reviews of Modern Physics, 65(2): 413–497 (1993) [13] Albrecht, T. R., et al. Frequency modulation detection using high‐Q cantilevers for enhanced force microscope sensitivity, Journal of Applied Physics 69(2): 668-673 (1991) [14] Nony, L., et al. A nc-AFM simulator with Phase Locked Loop-controlled frequency detection and excitation, arxiv preprint https://arxiv.org/abs/physics/0701343 (2007) [15] Stange et al. Building a Casimir metrology platform using a commercial MEMS sensor Microsystems & Nanoengineering (2019) [16] H. B. Chan, et. al. Quantum Mechanical Actuation of Microelectromechanical Systems by the Casimir Force, Science 291:1941-1944 (2001) [17] Advanced Magnets Co. Typical Physical and Chemical Properties of Some Magnetic Materials. https://www.advancedmagnets.com/custom-magnets/ (2022) [Accessed Jan. 29, 2024]. [18] Javor, J. et al. 100 pT/cm single-point MEMS magnetic gradiometer from a commercial accelerometer. Microsyst. Nanoeng. 6, 1–13 (2020) [19] Porr B, et. al. Real-time noise cancellation with deep learning, PLoS One (2022) Zhang, X., et al. Precision measurement and frequency metrology with ultracold atoms, National Science Review 3:189–200 (2016) [6] Chang, L. Foundations of MEMS (Second Edition), Pearson Education Asia (2012) [7] Asztalos, S. J. et al. A SQUID-based microwave cavity search for dark-matter axions, Physical Review Letters, 104 (4) (2010) [8] K. D. Irwin et al. Transition-edge sensors, Cryogenic Particle Detection, Springer (2005) [9] East Asian Observatory SCUBA-2. https://www.eaobservatory.org/jcmt/instrumentation/continuum/scuba-2/ (2019) [Accessed May 17, 2024] [10] Yao, X. et al. Background noise estimation of the geomagnetic signal, Geosci. Instrum. Method. Data Syst., 7, 189–193 (2018) [11] Swain, P. P. et al. A feasibility study to measure magnetocardiography (MCG) in unshielded environment using first order gradiometer, Biomed. Signal Process. Control 55, 101664 (2020) [12] Hämäläinen, M., et al. Magnetoencephalography — theory, instrumentation, and applications to noninvasive studies of the working human brain, Reviews of Modern Physics, 65(2): 413–497 (1993) [13] Albrecht, T. R., et al. Frequency modulation detection using high‐Q cantilevers for enhanced force microscope sensitivity, Journal of Applied Physics 69(2): 668-673 (1991) [14] Nony, L., et al. A nc-AFM simulator with Phase Locked Loop-controlled frequency detection and excitation, arxiv preprint https://arxiv.org/abs/physics/0701343 (2007) [15] Stange et al. Building a Casimir metrology platform using a commercial MEMS sensor Microsystems & Nanoengineering (2019) [16] H. B. Chan, et. al. Quantum Mechanical Actuation of Microelectromechanical Systems by the Casimir Force, Science 291:1941-1944 (2001) [17] Advanced Magnets Co. Typical Physical and Chemical Properties of Some Magnetic Materials. https://www.advancedmagnets.com/custom-magnets/ (2022) [Accessed Jan. 29, 2024]. [18] Javor, J. et al. 100 pT/cm single-point MEMS magnetic gradiometer from a commercial accelerometer. Microsyst. Nanoeng. 6, 1–13 (2020) [19] Porr B, et. al. Real-time noise cancellation with deep learning, PLoS One (2022) Chang, L. Foundations of MEMS (Second Edition), Pearson Education Asia (2012) [7] Asztalos, S. J. et al. A SQUID-based microwave cavity search for dark-matter axions, Physical Review Letters, 104 (4) (2010) [8] K. D. Irwin et al. Transition-edge sensors, Cryogenic Particle Detection, Springer (2005) [9] East Asian Observatory SCUBA-2. https://www.eaobservatory.org/jcmt/instrumentation/continuum/scuba-2/ (2019) [Accessed May 17, 2024] [10] Yao, X. et al. Background noise estimation of the geomagnetic signal, Geosci. Instrum. Method. Data Syst., 7, 189–193 (2018) [11] Swain, P. P. et al. A feasibility study to measure magnetocardiography (MCG) in unshielded environment using first order gradiometer, Biomed. Signal Process. Control 55, 101664 (2020) [12] Hämäläinen, M., et al. Magnetoencephalography — theory, instrumentation, and applications to noninvasive studies of the working human brain, Reviews of Modern Physics, 65(2): 413–497 (1993) [13] Albrecht, T. R., et al. Frequency modulation detection using high‐Q cantilevers for enhanced force microscope sensitivity, Journal of Applied Physics 69(2): 668-673 (1991) [14] Nony, L., et al. A nc-AFM simulator with Phase Locked Loop-controlled frequency detection and excitation, arxiv preprint https://arxiv.org/abs/physics/0701343 (2007) [15] Stange et al. Building a Casimir metrology platform using a commercial MEMS sensor Microsystems & Nanoengineering (2019) [16] H. B. Chan, et. al. Quantum Mechanical Actuation of Microelectromechanical Systems by the Casimir Force, Science 291:1941-1944 (2001) [17] Advanced Magnets Co. Typical Physical and Chemical Properties of Some Magnetic Materials. https://www.advancedmagnets.com/custom-magnets/ (2022) [Accessed Jan. 29, 2024]. [18] Javor, J. et al. 100 pT/cm single-point MEMS magnetic gradiometer from a commercial accelerometer. Microsyst. Nanoeng. 6, 1–13 (2020) [19] Porr B, et. al. Real-time noise cancellation with deep learning, PLoS One (2022) Asztalos, S. J. et al. A SQUID-based microwave cavity search for dark-matter axions, Physical Review Letters, 104 (4) (2010) [8] K. D. Irwin et al. Transition-edge sensors, Cryogenic Particle Detection, Springer (2005) [9] East Asian Observatory SCUBA-2. https://www.eaobservatory.org/jcmt/instrumentation/continuum/scuba-2/ (2019) [Accessed May 17, 2024] [10] Yao, X. et al. Background noise estimation of the geomagnetic signal, Geosci. Instrum. Method. Data Syst., 7, 189–193 (2018) [11] Swain, P. P. et al. A feasibility study to measure magnetocardiography (MCG) in unshielded environment using first order gradiometer, Biomed. Signal Process. Control 55, 101664 (2020) [12] Hämäläinen, M., et al. Magnetoencephalography — theory, instrumentation, and applications to noninvasive studies of the working human brain, Reviews of Modern Physics, 65(2): 413–497 (1993) [13] Albrecht, T. R., et al. Frequency modulation detection using high‐Q cantilevers for enhanced force microscope sensitivity, Journal of Applied Physics 69(2): 668-673 (1991) [14] Nony, L., et al. A nc-AFM simulator with Phase Locked Loop-controlled frequency detection and excitation, arxiv preprint https://arxiv.org/abs/physics/0701343 (2007) [15] Stange et al. Building a Casimir metrology platform using a commercial MEMS sensor Microsystems & Nanoengineering (2019) [16] H. B. Chan, et. al. Quantum Mechanical Actuation of Microelectromechanical Systems by the Casimir Force, Science 291:1941-1944 (2001) [17] Advanced Magnets Co. Typical Physical and Chemical Properties of Some Magnetic Materials. https://www.advancedmagnets.com/custom-magnets/ (2022) [Accessed Jan. 29, 2024]. [18] Javor, J. et al. 100 pT/cm single-point MEMS magnetic gradiometer from a commercial accelerometer. Microsyst. Nanoeng. 6, 1–13 (2020) [19] Porr B, et. al. Real-time noise cancellation with deep learning, PLoS One (2022) K. D. Irwin et al. Transition-edge sensors, Cryogenic Particle Detection, Springer (2005) [9] East Asian Observatory SCUBA-2. https://www.eaobservatory.org/jcmt/instrumentation/continuum/scuba-2/ (2019) [Accessed May 17, 2024] [10] Yao, X. et al. Background noise estimation of the geomagnetic signal, Geosci. Instrum. Method. Data Syst., 7, 189–193 (2018) [11] Swain, P. P. et al. 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Magnetoencephalography — theory, instrumentation, and applications to noninvasive studies of the working human brain, Reviews of Modern Physics, 65(2): 413–497 (1993) [13] Albrecht, T. R., et al. Frequency modulation detection using high‐Q cantilevers for enhanced force microscope sensitivity, Journal of Applied Physics 69(2): 668-673 (1991) [14] Nony, L., et al. A nc-AFM simulator with Phase Locked Loop-controlled frequency detection and excitation, arxiv preprint https://arxiv.org/abs/physics/0701343 (2007) [15] Stange et al. Building a Casimir metrology platform using a commercial MEMS sensor Microsystems & Nanoengineering (2019) [16] H. B. Chan, et. al. Quantum Mechanical Actuation of Microelectromechanical Systems by the Casimir Force, Science 291:1941-1944 (2001) [17] Advanced Magnets Co. Typical Physical and Chemical Properties of Some Magnetic Materials. https://www.advancedmagnets.com/custom-magnets/ (2022) [Accessed Jan. 29, 2024]. [18] Javor, J. et al. 100 pT/cm single-point MEMS magnetic gradiometer from a commercial accelerometer. Microsyst. Nanoeng. 6, 1–13 (2020) [19] Porr B, et. al. Real-time noise cancellation with deep learning, PLoS One (2022) Yao, X. et al. Background noise estimation of the geomagnetic signal, Geosci. Instrum. Method. Data Syst., 7, 189–193 (2018) [11] Swain, P. P. et al. A feasibility study to measure magnetocardiography (MCG) in unshielded environment using first order gradiometer, Biomed. Signal Process. Control 55, 101664 (2020) [12] Hämäläinen, M., et al. Magnetoencephalography — theory, instrumentation, and applications to noninvasive studies of the working human brain, Reviews of Modern Physics, 65(2): 413–497 (1993) [13] Albrecht, T. R., et al. Frequency modulation detection using high‐Q cantilevers for enhanced force microscope sensitivity, Journal of Applied Physics 69(2): 668-673 (1991) [14] Nony, L., et al. A nc-AFM simulator with Phase Locked Loop-controlled frequency detection and excitation, arxiv preprint https://arxiv.org/abs/physics/0701343 (2007) [15] Stange et al. Building a Casimir metrology platform using a commercial MEMS sensor Microsystems & Nanoengineering (2019) [16] H. B. Chan, et. al. Quantum Mechanical Actuation of Microelectromechanical Systems by the Casimir Force, Science 291:1941-1944 (2001) [17] Advanced Magnets Co. Typical Physical and Chemical Properties of Some Magnetic Materials. https://www.advancedmagnets.com/custom-magnets/ (2022) [Accessed Jan. 29, 2024]. [18] Javor, J. et al. 100 pT/cm single-point MEMS magnetic gradiometer from a commercial accelerometer. Microsyst. Nanoeng. 6, 1–13 (2020) [19] Porr B, et. al. Real-time noise cancellation with deep learning, PLoS One (2022) Swain, P. P. et al. A feasibility study to measure magnetocardiography (MCG) in unshielded environment using first order gradiometer, Biomed. Signal Process. Control 55, 101664 (2020) [12] Hämäläinen, M., et al. Magnetoencephalography — theory, instrumentation, and applications to noninvasive studies of the working human brain, Reviews of Modern Physics, 65(2): 413–497 (1993) [13] Albrecht, T. R., et al. Frequency modulation detection using high‐Q cantilevers for enhanced force microscope sensitivity, Journal of Applied Physics 69(2): 668-673 (1991) [14] Nony, L., et al. A nc-AFM simulator with Phase Locked Loop-controlled frequency detection and excitation, arxiv preprint https://arxiv.org/abs/physics/0701343 (2007) [15] Stange et al. Building a Casimir metrology platform using a commercial MEMS sensor Microsystems & Nanoengineering (2019) [16] H. B. Chan, et. al. Quantum Mechanical Actuation of Microelectromechanical Systems by the Casimir Force, Science 291:1941-1944 (2001) [17] Advanced Magnets Co. Typical Physical and Chemical Properties of Some Magnetic Materials. https://www.advancedmagnets.com/custom-magnets/ (2022) [Accessed Jan. 29, 2024]. [18] Javor, J. et al. 100 pT/cm single-point MEMS magnetic gradiometer from a commercial accelerometer. Microsyst. Nanoeng. 6, 1–13 (2020) [19] Porr B, et. al. Real-time noise cancellation with deep learning, PLoS One (2022) Hämäläinen, M., et al. Magnetoencephalography — theory, instrumentation, and applications to noninvasive studies of the working human brain, Reviews of Modern Physics, 65(2): 413–497 (1993) [13] Albrecht, T. R., et al. Frequency modulation detection using high‐Q cantilevers for enhanced force microscope sensitivity, Journal of Applied Physics 69(2): 668-673 (1991) [14] Nony, L., et al. A nc-AFM simulator with Phase Locked Loop-controlled frequency detection and excitation, arxiv preprint https://arxiv.org/abs/physics/0701343 (2007) [15] Stange et al. 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A nc-AFM simulator with Phase Locked Loop-controlled frequency detection and excitation, arxiv preprint https://arxiv.org/abs/physics/0701343 (2007) [15] Stange et al. Building a Casimir metrology platform using a commercial MEMS sensor Microsystems & Nanoengineering (2019) [16] H. B. Chan, et. al. Quantum Mechanical Actuation of Microelectromechanical Systems by the Casimir Force, Science 291:1941-1944 (2001) [17] Advanced Magnets Co. Typical Physical and Chemical Properties of Some Magnetic Materials. https://www.advancedmagnets.com/custom-magnets/ (2022) [Accessed Jan. 29, 2024]. [18] Javor, J. et al. 100 pT/cm single-point MEMS magnetic gradiometer from a commercial accelerometer. Microsyst. Nanoeng. 6, 1–13 (2020) [19] Porr B, et. al. Real-time noise cancellation with deep learning, PLoS One (2022) Nony, L., et al. A nc-AFM simulator with Phase Locked Loop-controlled frequency detection and excitation, arxiv preprint https://arxiv.org/abs/physics/0701343 (2007) [15] Stange et al. Building a Casimir metrology platform using a commercial MEMS sensor Microsystems & Nanoengineering (2019) [16] H. B. Chan, et. al. Quantum Mechanical Actuation of Microelectromechanical Systems by the Casimir Force, Science 291:1941-1944 (2001) [17] Advanced Magnets Co. Typical Physical and Chemical Properties of Some Magnetic Materials. https://www.advancedmagnets.com/custom-magnets/ (2022) [Accessed Jan. 29, 2024]. [18] Javor, J. et al. 100 pT/cm single-point MEMS magnetic gradiometer from a commercial accelerometer. Microsyst. Nanoeng. 6, 1–13 (2020) [19] Porr B, et. al. Real-time noise cancellation with deep learning, PLoS One (2022) Stange et al. Building a Casimir metrology platform using a commercial MEMS sensor Microsystems & Nanoengineering (2019) [16] H. B. Chan, et. al. Quantum Mechanical Actuation of Microelectromechanical Systems by the Casimir Force, Science 291:1941-1944 (2001) [17] Advanced Magnets Co. 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Magnetoencephalography — theory, instrumentation, and applications to noninvasive studies of the working human brain, Reviews of Modern Physics, 65(2): 413–497 (1993) [13] Albrecht, T. R., et al. Frequency modulation detection using high‐Q cantilevers for enhanced force microscope sensitivity, Journal of Applied Physics 69(2): 668-673 (1991) [14] Nony, L., et al. A nc-AFM simulator with Phase Locked Loop-controlled frequency detection and excitation, arxiv preprint https://arxiv.org/abs/physics/0701343 (2007) [15] Stange et al. Building a Casimir metrology platform using a commercial MEMS sensor Microsystems & Nanoengineering (2019) [16] H. B. Chan, et. al. Quantum Mechanical Actuation of Microelectromechanical Systems by the Casimir Force, Science 291:1941-1944 (2001) [17] Advanced Magnets Co. Typical Physical and Chemical Properties of Some Magnetic Materials. https://www.advancedmagnets.com/custom-magnets/ (2022) [Accessed Jan. 29, 2024]. [18] Javor, J. et al. 100 pT/cm single-point MEMS magnetic gradiometer from a commercial accelerometer. Microsyst. Nanoeng. 6, 1–13 (2020) [19] Porr B, et. al. Real-time noise cancellation with deep learning, PLoS One (2022) Chang, L. Foundations of MEMS (Second Edition), Pearson Education Asia (2012) [7] Asztalos, S. J. et al. A SQUID-based microwave cavity search for dark-matter axions, Physical Review Letters, 104 (4) (2010) [8] K. D. Irwin et al. Transition-edge sensors, Cryogenic Particle Detection, Springer (2005) [9] East Asian Observatory SCUBA-2. https://www.eaobservatory.org/jcmt/instrumentation/continuum/scuba-2/ (2019) [Accessed May 17, 2024] [10] Yao, X. et al. Background noise estimation of the geomagnetic signal, Geosci. Instrum. Method. Data Syst., 7, 189–193 (2018) [11] Swain, P. P. et al. A feasibility study to measure magnetocardiography (MCG) in unshielded environment using first order gradiometer, Biomed. Signal Process. Control 55, 101664 (2020) [12] Hämäläinen, M., et al. Magnetoencephalography — theory, instrumentation, and applications to noninvasive studies of the working human brain, Reviews of Modern Physics, 65(2): 413–497 (1993) [13] Albrecht, T. R., et al. Frequency modulation detection using high‐Q cantilevers for enhanced force microscope sensitivity, Journal of Applied Physics 69(2): 668-673 (1991) [14] Nony, L., et al. A nc-AFM simulator with Phase Locked Loop-controlled frequency detection and excitation, arxiv preprint https://arxiv.org/abs/physics/0701343 (2007) [15] Stange et al. Building a Casimir metrology platform using a commercial MEMS sensor Microsystems & Nanoengineering (2019) [16] H. B. Chan, et. al. Quantum Mechanical Actuation of Microelectromechanical Systems by the Casimir Force, Science 291:1941-1944 (2001) [17] Advanced Magnets Co. Typical Physical and Chemical Properties of Some Magnetic Materials. https://www.advancedmagnets.com/custom-magnets/ (2022) [Accessed Jan. 29, 2024]. [18] Javor, J. et al. 100 pT/cm single-point MEMS magnetic gradiometer from a commercial accelerometer. Microsyst. Nanoeng. 6, 1–13 (2020) [19] Porr B, et. al. Real-time noise cancellation with deep learning, PLoS One (2022) Asztalos, S. J. et al. A SQUID-based microwave cavity search for dark-matter axions, Physical Review Letters, 104 (4) (2010) [8] K. D. Irwin et al. Transition-edge sensors, Cryogenic Particle Detection, Springer (2005) [9] East Asian Observatory SCUBA-2. https://www.eaobservatory.org/jcmt/instrumentation/continuum/scuba-2/ (2019) [Accessed May 17, 2024] [10] Yao, X. et al. Background noise estimation of the geomagnetic signal, Geosci. Instrum. Method. Data Syst., 7, 189–193 (2018) [11] Swain, P. P. et al. A feasibility study to measure magnetocardiography (MCG) in unshielded environment using first order gradiometer, Biomed. Signal Process. Control 55, 101664 (2020) [12] Hämäläinen, M., et al. Magnetoencephalography — theory, instrumentation, and applications to noninvasive studies of the working human brain, Reviews of Modern Physics, 65(2): 413–497 (1993) [13] Albrecht, T. R., et al. Frequency modulation detection using high‐Q cantilevers for enhanced force microscope sensitivity, Journal of Applied Physics 69(2): 668-673 (1991) [14] Nony, L., et al. A nc-AFM simulator with Phase Locked Loop-controlled frequency detection and excitation, arxiv preprint https://arxiv.org/abs/physics/0701343 (2007) [15] Stange et al. Building a Casimir metrology platform using a commercial MEMS sensor Microsystems & Nanoengineering (2019) [16] H. B. Chan, et. al. Quantum Mechanical Actuation of Microelectromechanical Systems by the Casimir Force, Science 291:1941-1944 (2001) [17] Advanced Magnets Co. Typical Physical and Chemical Properties of Some Magnetic Materials. https://www.advancedmagnets.com/custom-magnets/ (2022) [Accessed Jan. 29, 2024]. [18] Javor, J. et al. 100 pT/cm single-point MEMS magnetic gradiometer from a commercial accelerometer. Microsyst. Nanoeng. 6, 1–13 (2020) [19] Porr B, et. al. Real-time noise cancellation with deep learning, PLoS One (2022) K. D. Irwin et al. Transition-edge sensors, Cryogenic Particle Detection, Springer (2005) [9] East Asian Observatory SCUBA-2. https://www.eaobservatory.org/jcmt/instrumentation/continuum/scuba-2/ (2019) [Accessed May 17, 2024] [10] Yao, X. et al. Background noise estimation of the geomagnetic signal, Geosci. Instrum. Method. Data Syst., 7, 189–193 (2018) [11] Swain, P. P. et al. A feasibility study to measure magnetocardiography (MCG) in unshielded environment using first order gradiometer, Biomed. Signal Process. Control 55, 101664 (2020) [12] Hämäläinen, M., et al. Magnetoencephalography — theory, instrumentation, and applications to noninvasive studies of the working human brain, Reviews of Modern Physics, 65(2): 413–497 (1993) [13] Albrecht, T. R., et al. Frequency modulation detection using high‐Q cantilevers for enhanced force microscope sensitivity, Journal of Applied Physics 69(2): 668-673 (1991) [14] Nony, L., et al. A nc-AFM simulator with Phase Locked Loop-controlled frequency detection and excitation, arxiv preprint https://arxiv.org/abs/physics/0701343 (2007) [15] Stange et al. Building a Casimir metrology platform using a commercial MEMS sensor Microsystems & Nanoengineering (2019) [16] H. B. Chan, et. al. Quantum Mechanical Actuation of Microelectromechanical Systems by the Casimir Force, Science 291:1941-1944 (2001) [17] Advanced Magnets Co. Typical Physical and Chemical Properties of Some Magnetic Materials. https://www.advancedmagnets.com/custom-magnets/ (2022) [Accessed Jan. 29, 2024]. [18] Javor, J. et al. 100 pT/cm single-point MEMS magnetic gradiometer from a commercial accelerometer. Microsyst. Nanoeng. 6, 1–13 (2020) [19] Porr B, et. al. Real-time noise cancellation with deep learning, PLoS One (2022) East Asian Observatory SCUBA-2. https://www.eaobservatory.org/jcmt/instrumentation/continuum/scuba-2/ (2019) [Accessed May 17, 2024] [10] Yao, X. et al. Background noise estimation of the geomagnetic signal, Geosci. Instrum. Method. Data Syst., 7, 189–193 (2018) [11] Swain, P. P. et al. A feasibility study to measure magnetocardiography (MCG) in unshielded environment using first order gradiometer, Biomed. Signal Process. Control 55, 101664 (2020) [12] Hämäläinen, M., et al. Magnetoencephalography — theory, instrumentation, and applications to noninvasive studies of the working human brain, Reviews of Modern Physics, 65(2): 413–497 (1993) [13] Albrecht, T. R., et al. Frequency modulation detection using high‐Q cantilevers for enhanced force microscope sensitivity, Journal of Applied Physics 69(2): 668-673 (1991) [14] Nony, L., et al. A nc-AFM simulator with Phase Locked Loop-controlled frequency detection and excitation, arxiv preprint https://arxiv.org/abs/physics/0701343 (2007) [15] Stange et al. Building a Casimir metrology platform using a commercial MEMS sensor Microsystems & Nanoengineering (2019) [16] H. B. Chan, et. al. Quantum Mechanical Actuation of Microelectromechanical Systems by the Casimir Force, Science 291:1941-1944 (2001) [17] Advanced Magnets Co. Typical Physical and Chemical Properties of Some Magnetic Materials. https://www.advancedmagnets.com/custom-magnets/ (2022) [Accessed Jan. 29, 2024]. [18] Javor, J. et al. 100 pT/cm single-point MEMS magnetic gradiometer from a commercial accelerometer. Microsyst. Nanoeng. 6, 1–13 (2020) [19] Porr B, et. al. Real-time noise cancellation with deep learning, PLoS One (2022) Yao, X. et al. Background noise estimation of the geomagnetic signal, Geosci. Instrum. Method. Data Syst., 7, 189–193 (2018) [11] Swain, P. P. et al. A feasibility study to measure magnetocardiography (MCG) in unshielded environment using first order gradiometer, Biomed. Signal Process. Control 55, 101664 (2020) [12] Hämäläinen, M., et al. Magnetoencephalography — theory, instrumentation, and applications to noninvasive studies of the working human brain, Reviews of Modern Physics, 65(2): 413–497 (1993) [13] Albrecht, T. R., et al. Frequency modulation detection using high‐Q cantilevers for enhanced force microscope sensitivity, Journal of Applied Physics 69(2): 668-673 (1991) [14] Nony, L., et al. A nc-AFM simulator with Phase Locked Loop-controlled frequency detection and excitation, arxiv preprint https://arxiv.org/abs/physics/0701343 (2007) [15] Stange et al. Building a Casimir metrology platform using a commercial MEMS sensor Microsystems & Nanoengineering (2019) [16] H. B. Chan, et. al. Quantum Mechanical Actuation of Microelectromechanical Systems by the Casimir Force, Science 291:1941-1944 (2001) [17] Advanced Magnets Co. Typical Physical and Chemical Properties of Some Magnetic Materials. https://www.advancedmagnets.com/custom-magnets/ (2022) [Accessed Jan. 29, 2024]. [18] Javor, J. et al. 100 pT/cm single-point MEMS magnetic gradiometer from a commercial accelerometer. Microsyst. Nanoeng. 6, 1–13 (2020) [19] Porr B, et. al. Real-time noise cancellation with deep learning, PLoS One (2022) Swain, P. P. et al. A feasibility study to measure magnetocardiography (MCG) in unshielded environment using first order gradiometer, Biomed. Signal Process. Control 55, 101664 (2020) [12] Hämäläinen, M., et al. Magnetoencephalography — theory, instrumentation, and applications to noninvasive studies of the working human brain, Reviews of Modern Physics, 65(2): 413–497 (1993) [13] Albrecht, T. R., et al. Frequency modulation detection using high‐Q cantilevers for enhanced force microscope sensitivity, Journal of Applied Physics 69(2): 668-673 (1991) [14] Nony, L., et al. A nc-AFM simulator with Phase Locked Loop-controlled frequency detection and excitation, arxiv preprint https://arxiv.org/abs/physics/0701343 (2007) [15] Stange et al. Building a Casimir metrology platform using a commercial MEMS sensor Microsystems & Nanoengineering (2019) [16] H. B. Chan, et. al. Quantum Mechanical Actuation of Microelectromechanical Systems by the Casimir Force, Science 291:1941-1944 (2001) [17] Advanced Magnets Co. Typical Physical and Chemical Properties of Some Magnetic Materials. https://www.advancedmagnets.com/custom-magnets/ (2022) [Accessed Jan. 29, 2024]. [18] Javor, J. et al. 100 pT/cm single-point MEMS magnetic gradiometer from a commercial accelerometer. Microsyst. Nanoeng. 6, 1–13 (2020) [19] Porr B, et. al. 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Irwin et al. Transition-edge sensors, Cryogenic Particle Detection, Springer (2005) [9] East Asian Observatory SCUBA-2. https://www.eaobservatory.org/jcmt/instrumentation/continuum/scuba-2/ (2019) [Accessed May 17, 2024] [10] Yao, X. et al. Background noise estimation of the geomagnetic signal, Geosci. Instrum. Method. Data Syst., 7, 189–193 (2018) [11] Swain, P. P. et al. A feasibility study to measure magnetocardiography (MCG) in unshielded environment using first order gradiometer, Biomed. Signal Process. Control 55, 101664 (2020) [12] Hämäläinen, M., et al. Magnetoencephalography — theory, instrumentation, and applications to noninvasive studies of the working human brain, Reviews of Modern Physics, 65(2): 413–497 (1993) [13] Albrecht, T. R., et al. Frequency modulation detection using high‐Q cantilevers for enhanced force microscope sensitivity, Journal of Applied Physics 69(2): 668-673 (1991) [14] Nony, L., et al. 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R., et al. Frequency modulation detection using high‐Q cantilevers for enhanced force microscope sensitivity, Journal of Applied Physics 69(2): 668-673 (1991) [14] Nony, L., et al. A nc-AFM simulator with Phase Locked Loop-controlled frequency detection and excitation, arxiv preprint https://arxiv.org/abs/physics/0701343 (2007) [15] Stange et al. Building a Casimir metrology platform using a commercial MEMS sensor Microsystems & Nanoengineering (2019) [16] H. B. Chan, et. al. Quantum Mechanical Actuation of Microelectromechanical Systems by the Casimir Force, Science 291:1941-1944 (2001) [17] Advanced Magnets Co. Typical Physical and Chemical Properties of Some Magnetic Materials. https://www.advancedmagnets.com/custom-magnets/ (2022) [Accessed Jan. 29, 2024]. [18] Javor, J. et al. 100 pT/cm single-point MEMS magnetic gradiometer from a commercial accelerometer. Microsyst. Nanoeng. 6, 1–13 (2020) [19] Porr B, et. al. Real-time noise cancellation with deep learning, PLoS One (2022) Nony, L., et al. A nc-AFM simulator with Phase Locked Loop-controlled frequency detection and excitation, arxiv preprint https://arxiv.org/abs/physics/0701343 (2007) [15] Stange et al. Building a Casimir metrology platform using a commercial MEMS sensor Microsystems & Nanoengineering (2019) [16] H. B. Chan, et. al. Quantum Mechanical Actuation of Microelectromechanical Systems by the Casimir Force, Science 291:1941-1944 (2001) [17] Advanced Magnets Co. Typical Physical and Chemical Properties of Some Magnetic Materials. https://www.advancedmagnets.com/custom-magnets/ (2022) [Accessed Jan. 29, 2024]. [18] Javor, J. et al. 100 pT/cm single-point MEMS magnetic gradiometer from a commercial accelerometer. Microsyst. Nanoeng. 6, 1–13 (2020) [19] Porr B, et. al. Real-time noise cancellation with deep learning, PLoS One (2022) Stange et al. 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Quantum Mechanical Actuation of Microelectromechanical Systems by the Casimir Force, Science 291:1941-1944 (2001) [17] Advanced Magnets Co. Typical Physical and Chemical Properties of Some Magnetic Materials. https://www.advancedmagnets.com/custom-magnets/ (2022) [Accessed Jan. 29, 2024]. [18] Javor, J. et al. 100 pT/cm single-point MEMS magnetic gradiometer from a commercial accelerometer. Microsyst. Nanoeng. 6, 1–13 (2020) [19] Porr B, et. al. Real-time noise cancellation with deep learning, PLoS One (2022) Hämäläinen, M., et al. Magnetoencephalography — theory, instrumentation, and applications to noninvasive studies of the working human brain, Reviews of Modern Physics, 65(2): 413–497 (1993) [13] Albrecht, T. R., et al. Frequency modulation detection using high‐Q cantilevers for enhanced force microscope sensitivity, Journal of Applied Physics 69(2): 668-673 (1991) [14] Nony, L., et al. 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Real-time noise cancellation with deep learning, PLoS One (2022) Nony, L., et al. A nc-AFM simulator with Phase Locked Loop-controlled frequency detection and excitation, arxiv preprint https://arxiv.org/abs/physics/0701343 (2007) [15] Stange et al. Building a Casimir metrology platform using a commercial MEMS sensor Microsystems & Nanoengineering (2019) [16] H. B. Chan, et. al. Quantum Mechanical Actuation of Microelectromechanical Systems by the Casimir Force, Science 291:1941-1944 (2001) [17] Advanced Magnets Co. Typical Physical and Chemical Properties of Some Magnetic Materials. https://www.advancedmagnets.com/custom-magnets/ (2022) [Accessed Jan. 29, 2024]. [18] Javor, J. et al. 100 pT/cm single-point MEMS magnetic gradiometer from a commercial accelerometer. Microsyst. Nanoeng. 6, 1–13 (2020) [19] Porr B, et. al. Real-time noise cancellation with deep learning, PLoS One (2022) Stange et al. 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[18] Javor, J. et al. 100 pT/cm single-point MEMS magnetic gradiometer from a commercial accelerometer. Microsyst. Nanoeng. 6, 1–13 (2020) [19] Porr B, et. al. Real-time noise cancellation with deep learning, PLoS One (2022) Advanced Magnets Co. Typical Physical and Chemical Properties of Some Magnetic Materials. https://www.advancedmagnets.com/custom-magnets/ (2022) [Accessed Jan. 29, 2024]. [18] Javor, J. et al. 100 pT/cm single-point MEMS magnetic gradiometer from a commercial accelerometer. Microsyst. Nanoeng. 6, 1–13 (2020) [19] Porr B, et. al. Real-time noise cancellation with deep learning, PLoS One (2022) Javor, J. et al. 100 pT/cm single-point MEMS magnetic gradiometer from a commercial accelerometer. Microsyst. Nanoeng. 6, 1–13 (2020) [19] Porr B, et. al. Real-time noise cancellation with deep learning, PLoS One (2022) Porr B, et. al. Real-time noise cancellation with deep learning, PLoS One (2022)
  10. Hämäläinen, M., et al. Magnetoencephalography — theory, instrumentation, and applications to noninvasive studies of the working human brain, Reviews of Modern Physics, 65(2): 413–497 (1993) [13] Albrecht, T. R., et al. Frequency modulation detection using high‐Q cantilevers for enhanced force microscope sensitivity, Journal of Applied Physics 69(2): 668-673 (1991) [14] Nony, L., et al. A nc-AFM simulator with Phase Locked Loop-controlled frequency detection and excitation, arxiv preprint https://arxiv.org/abs/physics/0701343 (2007) [15] Stange et al. Building a Casimir metrology platform using a commercial MEMS sensor Microsystems & Nanoengineering (2019) [16] H. B. Chan, et. al. Quantum Mechanical Actuation of Microelectromechanical Systems by the Casimir Force, Science 291:1941-1944 (2001) [17] Advanced Magnets Co. Typical Physical and Chemical Properties of Some Magnetic Materials. https://www.advancedmagnets.com/custom-magnets/ (2022) [Accessed Jan. 29, 2024]. [18] Javor, J. et al. 100 pT/cm single-point MEMS magnetic gradiometer from a commercial accelerometer. Microsyst. Nanoeng. 6, 1–13 (2020) [19] Porr B, et. al. Real-time noise cancellation with deep learning, PLoS One (2022) Albrecht, T. R., et al. Frequency modulation detection using high‐Q cantilevers for enhanced force microscope sensitivity, Journal of Applied Physics 69(2): 668-673 (1991) [14] Nony, L., et al. A nc-AFM simulator with Phase Locked Loop-controlled frequency detection and excitation, arxiv preprint https://arxiv.org/abs/physics/0701343 (2007) [15] Stange et al. Building a Casimir metrology platform using a commercial MEMS sensor Microsystems & Nanoengineering (2019) [16] H. B. Chan, et. al. Quantum Mechanical Actuation of Microelectromechanical Systems by the Casimir Force, Science 291:1941-1944 (2001) [17] Advanced Magnets Co. Typical Physical and Chemical Properties of Some Magnetic Materials. https://www.advancedmagnets.com/custom-magnets/ (2022) [Accessed Jan. 29, 2024]. [18] Javor, J. et al. 100 pT/cm single-point MEMS magnetic gradiometer from a commercial accelerometer. Microsyst. Nanoeng. 6, 1–13 (2020) [19] Porr B, et. al. Real-time noise cancellation with deep learning, PLoS One (2022) Nony, L., et al. A nc-AFM simulator with Phase Locked Loop-controlled frequency detection and excitation, arxiv preprint https://arxiv.org/abs/physics/0701343 (2007) [15] Stange et al. Building a Casimir metrology platform using a commercial MEMS sensor Microsystems & Nanoengineering (2019) [16] H. B. Chan, et. al. Quantum Mechanical Actuation of Microelectromechanical Systems by the Casimir Force, Science 291:1941-1944 (2001) [17] Advanced Magnets Co. Typical Physical and Chemical Properties of Some Magnetic Materials. https://www.advancedmagnets.com/custom-magnets/ (2022) [Accessed Jan. 29, 2024]. [18] Javor, J. et al. 100 pT/cm single-point MEMS magnetic gradiometer from a commercial accelerometer. Microsyst. Nanoeng. 6, 1–13 (2020) [19] Porr B, et. al. Real-time noise cancellation with deep learning, PLoS One (2022) Stange et al. Building a Casimir metrology platform using a commercial MEMS sensor Microsystems & Nanoengineering (2019) [16] H. B. Chan, et. al. Quantum Mechanical Actuation of Microelectromechanical Systems by the Casimir Force, Science 291:1941-1944 (2001) [17] Advanced Magnets Co. Typical Physical and Chemical Properties of Some Magnetic Materials. https://www.advancedmagnets.com/custom-magnets/ (2022) [Accessed Jan. 29, 2024]. [18] Javor, J. et al. 100 pT/cm single-point MEMS magnetic gradiometer from a commercial accelerometer. Microsyst. Nanoeng. 6, 1–13 (2020) [19] Porr B, et. al. Real-time noise cancellation with deep learning, PLoS One (2022) H. B. Chan, et. al. Quantum Mechanical Actuation of Microelectromechanical Systems by the Casimir Force, Science 291:1941-1944 (2001) [17] Advanced Magnets Co. Typical Physical and Chemical Properties of Some Magnetic Materials. https://www.advancedmagnets.com/custom-magnets/ (2022) [Accessed Jan. 29, 2024]. [18] Javor, J. et al. 100 pT/cm single-point MEMS magnetic gradiometer from a commercial accelerometer. Microsyst. Nanoeng. 6, 1–13 (2020) [19] Porr B, et. al. Real-time noise cancellation with deep learning, PLoS One (2022) Advanced Magnets Co. Typical Physical and Chemical Properties of Some Magnetic Materials. https://www.advancedmagnets.com/custom-magnets/ (2022) [Accessed Jan. 29, 2024]. [18] Javor, J. et al. 100 pT/cm single-point MEMS magnetic gradiometer from a commercial accelerometer. Microsyst. Nanoeng. 6, 1–13 (2020) [19] Porr B, et. al. Real-time noise cancellation with deep learning, PLoS One (2022) Javor, J. et al. 100 pT/cm single-point MEMS magnetic gradiometer from a commercial accelerometer. Microsyst. Nanoeng. 6, 1–13 (2020) [19] Porr B, et. al. Real-time noise cancellation with deep learning, PLoS One (2022) Porr B, et. al. Real-time noise cancellation with deep learning, PLoS One (2022)
  11. Albrecht, T. R., et al. Frequency modulation detection using high‐Q cantilevers for enhanced force microscope sensitivity, Journal of Applied Physics 69(2): 668-673 (1991) [14] Nony, L., et al. A nc-AFM simulator with Phase Locked Loop-controlled frequency detection and excitation, arxiv preprint https://arxiv.org/abs/physics/0701343 (2007) [15] Stange et al. Building a Casimir metrology platform using a commercial MEMS sensor Microsystems & Nanoengineering (2019) [16] H. B. Chan, et. al. Quantum Mechanical Actuation of Microelectromechanical Systems by the Casimir Force, Science 291:1941-1944 (2001) [17] Advanced Magnets Co. Typical Physical and Chemical Properties of Some Magnetic Materials. https://www.advancedmagnets.com/custom-magnets/ (2022) [Accessed Jan. 29, 2024]. [18] Javor, J. et al. 100 pT/cm single-point MEMS magnetic gradiometer from a commercial accelerometer. Microsyst. Nanoeng. 6, 1–13 (2020) [19] Porr B, et. al. Real-time noise cancellation with deep learning, PLoS One (2022) Nony, L., et al. A nc-AFM simulator with Phase Locked Loop-controlled frequency detection and excitation, arxiv preprint https://arxiv.org/abs/physics/0701343 (2007) [15] Stange et al. Building a Casimir metrology platform using a commercial MEMS sensor Microsystems & Nanoengineering (2019) [16] H. B. Chan, et. al. Quantum Mechanical Actuation of Microelectromechanical Systems by the Casimir Force, Science 291:1941-1944 (2001) [17] Advanced Magnets Co. Typical Physical and Chemical Properties of Some Magnetic Materials. https://www.advancedmagnets.com/custom-magnets/ (2022) [Accessed Jan. 29, 2024]. [18] Javor, J. et al. 100 pT/cm single-point MEMS magnetic gradiometer from a commercial accelerometer. Microsyst. Nanoeng. 6, 1–13 (2020) [19] Porr B, et. al. Real-time noise cancellation with deep learning, PLoS One (2022) Stange et al. Building a Casimir metrology platform using a commercial MEMS sensor Microsystems & Nanoengineering (2019) [16] H. B. Chan, et. al. Quantum Mechanical Actuation of Microelectromechanical Systems by the Casimir Force, Science 291:1941-1944 (2001) [17] Advanced Magnets Co. Typical Physical and Chemical Properties of Some Magnetic Materials. https://www.advancedmagnets.com/custom-magnets/ (2022) [Accessed Jan. 29, 2024]. [18] Javor, J. et al. 100 pT/cm single-point MEMS magnetic gradiometer from a commercial accelerometer. Microsyst. Nanoeng. 6, 1–13 (2020) [19] Porr B, et. al. Real-time noise cancellation with deep learning, PLoS One (2022) H. B. Chan, et. al. Quantum Mechanical Actuation of Microelectromechanical Systems by the Casimir Force, Science 291:1941-1944 (2001) [17] Advanced Magnets Co. Typical Physical and Chemical Properties of Some Magnetic Materials. https://www.advancedmagnets.com/custom-magnets/ (2022) [Accessed Jan. 29, 2024]. [18] Javor, J. et al. 100 pT/cm single-point MEMS magnetic gradiometer from a commercial accelerometer. Microsyst. Nanoeng. 6, 1–13 (2020) [19] Porr B, et. al. Real-time noise cancellation with deep learning, PLoS One (2022) Advanced Magnets Co. Typical Physical and Chemical Properties of Some Magnetic Materials. https://www.advancedmagnets.com/custom-magnets/ (2022) [Accessed Jan. 29, 2024]. [18] Javor, J. et al. 100 pT/cm single-point MEMS magnetic gradiometer from a commercial accelerometer. Microsyst. Nanoeng. 6, 1–13 (2020) [19] Porr B, et. al. Real-time noise cancellation with deep learning, PLoS One (2022) Javor, J. et al. 100 pT/cm single-point MEMS magnetic gradiometer from a commercial accelerometer. Microsyst. Nanoeng. 6, 1–13 (2020) [19] Porr B, et. al. Real-time noise cancellation with deep learning, PLoS One (2022) Porr B, et. al. Real-time noise cancellation with deep learning, PLoS One (2022)
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