CRYOGENIC HYDROGEN MASER By . Martin Dominik Hiirlimann Dipl. Natw. ETH, Swiss Federal Institute of Technology, Zurich A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY in THE FACULTY OF GRADUATE STUDIES PHYSICS We accept this thesis as conforming to the required standard THE UNIVERSITY OF BRITISH COLUMBIA July 1989 © Martin Dominik Hiirlimann, 1989 In presenting this thesis in partial fulfilment of the requirements for an advanced degree at the University of British Columbia, I agree that the Library shall make it freely available for reference and study. I further agree that permission for extensive copying of this thesis for scholarly purposes may be granted by the head of my department or by his or her representatives. It is understood that copying or publication of this thesis for financial gain shall not be allowed without my written permission. Department The University of British Columbia Vancouver, Canada DE-6 (2/88) Abstract A new type of atomic hydrogen maser that operates in a dilution refrigerator has been developed. In this device, the hydrogen atoms circulate back and forth between a mi• crowave pumped state invertor in high field and the maser cavity in zero field. A prototype maser with a small maser cavity has been built and the results obtained so far are encouraging. Stable maser oscillations were observed for temperatures of the maser bulb between 230 mK and 660 mK and for densities up to 3 x 1012cm-3. The short term frequency stability was measured with the help of two high quality quartz crystal oscillators by the three-cornered-hat method. The observed fractional frequency fluctuations for an averaging time of 1 s were 6.3 ± 3.7 x 10-14, which is lower than the results from the best room temperature masers. In conjunction with the stability measurements, the phase noise of the maser electronics was investigated. In particular, the temperature dependence of the phase noise of the cooled preamplifier was measured and it was shown that anomalous high noise levels between 2.2 K and 4.2 K are caused by the boiling of the liquid helium. From the temperature dependence of the maser frequency, the binding energy EB of 4 H on He could be determined to a high precision. The result is EB = 1.011 ± 0.010 K. An extensive computer simulation program has been written that models the opera• tion of the cryogenic hydrogen maser. It has been used to analyze and interpret some of the data. In addition, this simulation program is helpful for the design of an improved second generation cryogenic maser. Based on the present data and the model calcula• tions, a new pumping scheme is proposed that is expected to increase the efficiency of the state invertor significantly. ii Table of Contents Abstract ii List of Tables vii List of Figures viii Acknowledgement x 1 Introduction 1 2 Theory of Maser Operation 8 2.1 Hyperfine states of atomic hydrogen 8 2.2 Interaction with rf magnetic field 11 2.3 Relaxation, Bloch equation 12 2.4 Stimulated emission 14 2.5 Power emitted by atoms 17 3 Properties of atomic hydrogen at low temperatures 20 3.1 Interactions with the walls 20 3.2 Recombination 23 3.3 Hyperfine frequency shift 25 3.4 Diffusion 27 3.5 Spin exchange 27 4 Considerations on frequency stability 32 iii 4.1 Characterization of frequency stability 32 4.2 Intrinsic frequency instabilities 33 4.3 Electronic Noise 35 4.4 Frequency shifts 38 4.4.1 Magnetic field shifts 38 4.4.2 Buffer gas and wall shifts 39 4.4.3 Cavity pulling and spin exchange shifts 40 5 The UBC cryogenic hydrogen maser 44 5.1 Principle of closed cycle cryogenic hydrogen maser 45 5.2 General characteristics of the design of the prototype apparatus 48 5.3 Maser cavity 51 5.3.1 Tuning and coupling of maser cavity 51 5.3.2 Maser bulb 54 5.3.3 Cooling bath 55 5.3.4 Thermometry 56 5.4 State selector 57 5.4.1 Microwave cavity 57 5.4.2 Relaxing foil 59 5.4.3 State selector magnet 59 5.5 Magnetic shielding of the maser cavity 61 5.6 Hydrogen discharge source 63 5.7 Electronics for state selector microwave pump 65 5.8 1420 MHz detection system 67 6 Experimental Results 73 6.1 Start up procedure 73 iv 6.1.1 Cool down 73 6.1.2 Adjustment of bias field at the maser cavity 74 6.1.3 Cross relaxation in the maser bulb 75 6.1.4 State selector magnetic field 79 6.2 Power versus density measurements 80 6.2.1 Density calibration 80 6.2.2 Recombination 85 6.2.3 Power output of maser 87 6.3 Temperature dependence of maser frequency 90 6.4 Frequency stability 96 6.4.1 Three-cornered-hat method 96 6.4.2 Details of stability measurements 98 6.4.3 Results of the stability measurements 100 6.5 Flicker phase noise measurements 105 6.5.1 Maser preamplifier 105 6.5.2 Phase noise of receiver 109 7 Computer simulation of the maser 113 7.1 Model of the maser 113 7.1.1 Flow 116 7.1.2 One-body spin relaxation 117 7.1.3 Microwave pumping in the state selector cavity 119 7.1.4 Spin exchange relaxation 120 7.1.5 Maser action 121 7.1.6 Overall rate equations 122 7.2 Results of the simulation 123 v 7.2.1 Choice of parameters 123 7.2.2 Power output of maser and state selector efficiency 125 7.2.3 Simulation results relevant for density calibration 128 8 Conclusions and outlook 131 8.1 The present cryogenic maser 131 8.2 Suggested improvements of the cryogenic maser design 132 8.2.1 Full size maser cavity . 132 8.2.2 Proposed new pumping scheme 133 8.2.3 Optimization of maser 135 8.3 Open questions 137 Appendices 138 A Magnetic moment operators 138 B The Slater equation 140 C Measures of frequency stability 143 D Magnetic field of a solenoid inside a long superconducting shield 147 E Eigenmodes of a sapphire loaded microwave cavity 153 E.l General Solution 153 E.2 Boundary conditions 156 E.3 Application to the cryogenic hydrogen maser 159 Bibliography 163 vi List of Tables 3.1 Binding energies of atomic hydrogen to different substrates 22 3.2 Calculated values of the spin exchange parameters 28 C.l Transformations between power-law spectral density and Allan vari• Sy(f) ance o-y2(r) 145 vii List of Figures 1.1 Basic scheme of the conventional hydrogen maser 2 2.1 Hyperfine energies as a function of magnetic field 10 2.2 Magnetization and effective magnetic field in rotating frame 15 5.1 Principle of UBC cryogenic hydrogen maser 46 5.2 Schematic drawing of relaxing foil 47 5.3 Simplified diagram of the cryogenic hydrogen maser 49 5.4 Design of maser cavity 52 5.5 Variable coupling assembly of maser cavity 53 5.6 Details of the state selector region 58 5.7 Low temperature atomic hydrogen discharge source 64 5.8 Schematics of the state selector pump electronics 66 5.9 Schematic diagram of the spectrometer 68 6.1 Transverse relaxation time versus bias field 76 6.2 Relaxation of longitudinal magnetization in the maser bulb versus time . 78 6.3 Maser resonance line width versus total density in the maser cavity ... 84 6.4 Decay of density in maser bulb while maser is oscillating 86 6.5 Output power of the maser versus total density of hydrogen atoms in the maser bulb 88 6.6 Observed frequency of the maser versus temperature of maser bulb ... 91 6.7 Fit to the observed temperature dependence of the maser frequency ... 94 viii 6.8 Compilation of reported values of the binding energy of H to 4He .... 95 6.9 Block diagrams of electronics used for measurement of frequency stability 99 6.10 Fractional frequency fluctuations of the cryogenic hydrogen maser and the two reference quartz crystal oscillators . 101 6.11 Relative frequency fluctuations versus averaging time for cryogenic hydro• gen maser and other high quality frequency sources . 103 6.12 Spectral density of phase fluctuations of maser preamplifier for different temperatures 107 6.13 Temperature dependence of spectral density of phase fluctuations of maser preamplifier near helium A-point . 108 6.14 Measured phase noise of various components of maser receiver 110 7.1 Model of cryogenic maser used in computer simulation 114 7.2 Calculated power output of maser versus density in maser bulb 126 7.3 Calculated population inversion outside the maser bulb 127 7.4 Calculated values of p$ + p^> versus density in maser bulb 128 7.5 Calculated density correction factors for the density calibration 129 B.l Electrical model of microwave cavity coupled to output electronics and containing rf magnetization Mz 142 D.l Solenoid inside superconducting shield 148 D. 2 Solenoid with correction coils inside superconducting shield 151 E. l Schematic drawing of the sapphire loaded microwave cavity 154 E.2 Length of the sapphire loaded cavity as a function of inner diameter . 160 E.3 Frequencies of all cavity modes below 2 GHz in the sapphire loaded cavity 162 ix Acknowledgement First of all, I would like to thank my 'Doktorvater' Walter Hardy who supervised this work over the last seven years. He conceived this project and his active participation in all aspects of the experiment were essential for its success.