Double-Resonance Magnetometry in Arbitrarily Oriented Fields. Stuart Ingleby University of Strathclyde

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1 Ingleby, Stuart and Riis, Erling and Arnold, Aidan and Griffin, Paul and O'Dwyer, Carolyn and Chalmers, Iain (2017) Double-resonance magnetometry in arbitrarily oriented fields. In: Workshop on Optically Pumped Magnetometers 2017, , University of Fribourg., This version is available at Strathprints is designed to allow users to access the research output of the University of Strathclyde. Unless otherwise explicitly stated on the manuscript, Copyright and Moral Rights for the papers on this site are retained by the individual authors and/or other copyright owners. Please check the manuscript for details of any other licences that may have been applied. You may not engage in further distribution of the material for any profitmaking activities or any commercial gain. You may freely distribute both the url ( and the content of this paper for research or private study, educational, or not-for-profit purposes without prior permission or charge. Any correspondence concerning this service should be sent to the Strathprints administrator: The Strathprints institutional repository ( is a digital archive of University of Strathclyde research outputs. It has been developed to disseminate open access research outputs, expose data about those outputs, and enable the management and persistent access to Strathclyde's intellectual output.

2 Double-Resonance Magnetometry in Arbitrarily Oriented Fields Stuart Ingleby University of Strathclyde

3 Overview Quantum Technology Hub Practical focus: apply QT to sensors Design choices Unshielded sensor B 0 orientation Signal amplitude and phase effects Exploitation Demonstrator system 20/08/17 Stuart Ingleby - Strathclyde University 2

4 Led Birmingham University Includes Strathclyde, Nottingham, Sussex, Southampton, NPL & industry Started Jan 2015 Unshielded portable sensor Geophysical measurement Low size, power requirement Sub-pT sensitivity 20/08/17 Stuart Ingleby - Strathclyde University 3

5 Unshielded Double Resonance Sensor Dynamic range - yes No requirement for µt compensation Noise rejection - yes Homodyne detection Polarimetry Gradiometry Arbitrary B 0 orientation -? Dead-zones Heading errors Portability - yes Single frequency pump-probe Firmware signal processing 20/08/17 Stuart Ingleby - Strathclyde University 4

6 Unshielded Double Resonance Sensor Dynamic range - yes No requirement for µt compensation Noise rejection - yes Homodyne detection Polarimetry Gradiometry Arbitrary B 0 orientation -? Dead-zones Heading errors Portability - yes Single frequency pump-probe Firmware signal processing 20/08/17 Stuart Ingleby - Strathclyde University 5

7 B 0 Orientation: Shielded Test System M x configuration Paraffin-coated Cs cell Weis group [1] B 0 control Software-controlled coils Iterative calibration Software modulation & demodulation Lineshape fitting [1] N. Castagna et al., Appl. Phys. B: Lasers Opt. 96, 763 (2009) 20/08/17 Stuart Ingleby - Strathclyde University 6

8 B 0 Orientation: Shielded Test System M x configuration Paraffin-coated Cs cell Weis group [] B 0 control Software-controlled coils Iterative calibration Software modulation & demodulation Lineshape fitting 20/08/17 Stuart Ingleby - Strathclyde University 7

9 B 0 Orientation: Shielded Test System B 0 control Low-noise current drivers Shield degauss Single-axis calibration [2] 3D calibration [C. O Dwyer poster] B 0 (µt) 200 nt B 0 δ B = 0.24 nt δθ = 0.23 mrad [2] S. J. Ingleby et al., Rev. Sci. Instrum. 88, (2017) 20/08/17 Stuart Ingleby - Strathclyde University 8

10 B 0 Orientation: Theory Pump Cs D1 4-3 σ-polarised 20 µw Γ PUMP << Γ Evolution B 0 >> B RF Ω RF ~ Γ Probe Polarimeter signal Linear dichroism Cancellation of! absorption 20/08/17 Stuart Ingleby - Strathclyde University 9

11 B 0 Orientation: Theory Multipole moment model [3][4] Pump Creation of k = 1,2 Equilibrium q = 0 B 0 frame Evolution RW frame B 0 // z B RF (t=0) // -x Obtain m kq (t) Probe Difference in and f (t) = m 2,0 (t) m = 3 2 m 2,0(t) 20/08/17 Stuart Ingleby - Strathclyde University 10 2,0 (t) d dt m k,q = q 3 8 [m 2,2(t) + m 2, 2 (t)] ρ = 2F k k=0 q= k m k,q T (k) q O (k) qq m k,q Ŵ (k) qq ( mk,q m eq k,q ), [3] A. Weis, G. Bison, A. S. Pazgalev, Phys. Rev. A 74, (2006) [4] M. A. Morrison and G. A. Parker, Aust. J. Phys. 40, 465 (1987)

12 B0 Orientation: Amplitude 4π angular scan Theory Ð 1646 resonance Þts Ð 3½ hours R X + Y Ð Extract X and Y from f(t) Dead-zones 20/08/17 Data Stuart Ingleby - Strathclyde University 11

13 B 0 Orientation: Phase Theory Data B RF // y-axis On-resonance phase tan φ X/Y, Strong dependence B 0 orientation B RF orientation tan φ RFy = 2sinθ L tan θ V (sin 2 θ L tan 2 θ V 1) cos θ L sinθ V tan φ RFz = sin 2θ L sinθ V (1 + cos 2 θ L )sin2θ V 20/08/17 Stuart Ingleby - Strathclyde University 12

14 B 0 Orientation: Phase Theory Data B RF // z-axis On-resonance phase tan φ X/Y, Strong dependence B 0 orientation B RF orientation tan φ RFy = tan φ RFz = 2sinθ L tan θ V (sin 2 θ L tan 2 θ V 1) cos θ L sinθ V sin 2θ L sinθ V (1 + cos 2 θ L )sin2θ V 20/08/17 Stuart Ingleby - Strathclyde University 13

15 Portable Demonstrator System Minimal hardware Ð VCSEL Ð MEMS cell Heater PCB Ð Polarimeter PCB Component testing Ð FPGA Ð MEMS cell Geometry Buffer gas 20/08/17 Stuart Ingleby - Strathclyde University 14

16 Summary Understanding B 0 orientation effects Model & measurement agree Optimal sensitivity axes Phase-vector information Exploit using signal processing Strathclyde Magnetometry People Erling Riis, Aidan Arnold, Paul Griffin, Stuart Ingleby, Dominic Hunter, Carolyn O Dwyer, Iain Chalmers 20/08/17 Stuart Ingleby - Strathclyde University 15