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  • Portable Atom Interferometry: Investigation on Magnetic Shielding Techniques for Compact Quantum Sensors

    by

    Georgios Voulazeris

    A thesis submitted to The University of Birmingham for the degree of DOCTOR OF PHILOSOPHY

    Ultracold Atoms Group School of Physics and Astronomy College of Engineering and Physical Sciences The University of Birmingham

    May 2018

  • University of Birmingham Research Archive

    e-theses repository This unpublished thesis/dissertation is copyright of the author and/or third parties. The intellectual property rights of the author or third parties in respect of this work are as defined by The Copyright Designs and Patents Act 1988 or as modified by any successor legislation. Any use made of information contained in this thesis/dissertation must be in accordance with that legislation and must be properly acknowledged. Further distribution or reproduction in any format is prohibited without the permission of the copyright holder.

  • To my family

  • CONTENTS

    1 Introduction and Motivation 3

    1.1 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

    1.2 Inertial Sensors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

    1.3 GGtop Consortium . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

    1.4 Thesis Organisation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

    1.5 Contribution Statement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

    2 Theory 11

    2.1 Fundamentals of Laser Cooling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

    2.1.1 Atom Cooling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

    2.1.2 Atom Trapping . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

    2.1.3 Sub–Doppler Cooling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

    2.2 Atom Interferometry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17

    2.2.1 Two-Level Atom . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18

    2.2.2 Raman Transitions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21

    2.2.3 Interferometric Sequence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23

    2.3 Interferometer Phase Contributions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25

    2.3.1 Gravitational Field . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27

    2.3.2 Magnetic Fields . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29

    2.4 Working With Rubidium–87 Species . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30

    2.5 Implications of a Portable Quantum Sensor . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31

    2.5.1 Temperature and Mechanical Factors . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32

    2.5.2 External Magnetic Fields . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32

    2.5.3 Impact of Magnetic Field Gradient Forces on the Interferometer . . . . . . . . . . . . 33

  • 3 Experimental Setup 37

    3.1 Physics Package . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37

    3.2 Vacuum Chamber System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39

    3.2.1 Telescopes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47

    3.3 Laser System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50

    3.4 Electronics Package . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53

    3.5 Interferometic Sequencies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55

    3.6 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56

    4 Magnetic Shielding 63

    4.1 Magnetic Shielding Fundamentals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64

    4.1.1 Analytical Treatment - Shielding Factors . . . . . . . . . . . . . . . . . . . . . . . . . 64

    4.1.2 Practical Challenges . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69

    4.1.3 Magnetic Permeability and Optimization . . . . . . . . . . . . . . . . . . . . . . . . . 70

    4.2 Numerical Treatment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73

    4.2.1 Model Definition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73

    4.3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76

    4.4 Shielding the GGtop Interferometer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81

    4.4.1 Calculations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82

    4.4.2 Experimental Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82

    4.5 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84

    5 Exploring Alternative Magnetic Shielding Techniques 89

    5.1 Lightweight Metglas Shielding Structures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89

    5.1.1 Experimental Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90

    5.1.2 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95

    5.2 3D-Printed Magnetic Shields for Compact Quantum Sensors . . . . . . . . . . . . . . . . . . . 98

    5.2.1 SLM Process Parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99

    5.2.2 Experimental Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100

    5.2.3 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109

    6 Final Discussion 111

    6.1 Summary on Findings and Considerations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112

  • 6.1.1 GGtop Experiment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112

    6.1.2 Magnetic Shielding . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115

    6.2 Recommendations for Future Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 120

    6.2.1 GGtop Experiment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 120

    6.2.2 Magnetic Shielding . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121

    6.3 Future Milestones . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122

    6.4 Other Positive Outcomes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123

    Appendix A Common Magnetic Shielding Materials I

    Appendix B Magnetic Measurements III

    Appendix C SLM Parameters for 3D Printed Shields V

    Appendix D Permalloy–80: Heat Treatment Cycles VII

    List of References IX

  • LIST OF FIGURES

    2.1 Schematic representation of the momentum exchange between an atom and the incident pho-

    tons from a near resonant light field. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

    2.2 Velocity dependent force for one–dimensional optical molasses. . . . . . . . . . . . . . . . . . 12

    2.3 Position dependent Zeeman effect caused by a linear magnetic field gradient B (z) to realize a

    magneto optical trap. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

    2.4 Sisyphus cooling mechanism. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

    2.5 σ+-σ− polarisation gradient cooling scheme. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17

    2.6 Mach–Zehnder interferometer scheme. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18

    2.7 Rabi state probability graph. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21

    2.8 Basic Raman transitions scheme of a three-level atom model. . . . . . . . . . . . . . . . . . . 21

    2.9 Co-propagating and counter-propagating Raman beam configurations. . . . . . . . . . . . . . 24

    2.10 Mach–Zehnder scheme for an atom interferometer based on stimulated Raman transitions. . . 25

    2.11 Theoretical example of Ramsey fringes produced by two successive π/2 pulses, separated by a

    free evolution time T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26

    2.12 Gravity signal of the Earth’s tides acquired after two days of gravity measurements at Stanford

    University (figure copied from [92]). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28

    2.13 Energy level scheme for 87Rb along with the experimental transitions. . . . . . . . . . . . . . 31

    2.14 Representation of the corresponding atomic angular momentum vectors for week magnetic fields. 34

    2.15 Considerations of the magnetic field gradient inside a magnetic shield that can induce accel-

    erations on the atoms due to the second order Zeeman eff

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