The Helmholtz coils

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Table of contents

Introduction
1 Context and principle
1.1 Theory of hydrogen energy levels
1.1.1 From the Bohr model to the Dirac equation
1.1.2 The Lamb shift
1.1.3 Hyperfine structure
1.2 Hydrogen spectroscopy and the proton radius puzzle
1.2.1 High-resolution spectroscopy
1.2.2 Determining the Rydberg constant
1.2.3 The proton radius puzzle
1.3 Our 1S−3S experiment
1.3.1 The second-order Doppler effect
1.3.2 Experimental improvements
1.3.3 Previous results and perspectives
2 The 1S−3S experimental setup
2.1 The 205-nm laser source
2.1.1 The titanium-sapphire laser
2.1.2 The frequency-doubled Verdi laser
2.1.3 Sum frequency generation
2.2 Frequency stabilization and scanning
2.2.1 The rubidium-stabilized standard laser
2.2.2 Ti:Sa and Verdi frequency stabilization
2.2.3 Frequency scanning
2.3 Frequency measurement
2.3.1 General principle
2.3.2 The frequency comb
2.3.3 The frequency beat notes
2.4 Excitation and detection
2.4.1 The atomic beam
2.4.2 The power build-up cavity
2.4.3 3S–2P fluorescence detection
2.5 Magnetic field production
2.5.1 The Helmholtz coils
2.5.2 Calibration of the magnetic field
2.6 Data acquisition and signals
2.6.1 Data acquisition
2.6.2 Observed signals
3 Systematic effects
3.1 The theoretical line profile
3.1.1 Fluorescence calculation
3.1.2 The velocity distribution
3.1.3 The complete fitting function
3.2 Shifting effects
3.2.1 Light shift
3.2.2 Pressure shift
3.3 Broadening effects
3.3.1 Saturation broadening
3.3.2 Transit-time broadening
3.3.3 Collisional broadening
3.3.4 Observed broadening
3.4 Cross-damping effect
3.4.1 Method
3.4.2 Details of the calculation
3.4.3 Results
4 Data analysis and results
4.1 Experimental data
4.1.1 Recordings
4.1.2 Fit with theoretical line profile
4.2 Determination of the velocity distribution
4.2.1 Chi-square minimization
4.2.2 Uncertainties
4.3 Correction of systematic effects
4.3.1 Light shift
4.3.2 Pressure shift
4.4 Final result
4.4.1 1S–3S transition frequency
4.4.2 Rydberg constant, Lamb shift and proton charge radius .
4.4.3 New analysis of Sandrine Galtier’s recordings
Conclusion
A Estimate of cross-damping shift
B Integration of the fluorescence over the detection region
C Least-squares method and uncertainties
Bibliography