IMPERIAL COLLEGE LONDON New Physics with Cold Molecules: Precise Microwave Spectroscopy of CH and the Development of a Microwave Trap by Stefan Truppe Thesis submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy in the Department of Physics November 2014 Declaration of Authorship I declare that this thesis is my own work. Where I have used the work of others the sources are appropriately referenced and acknowledged. The copyright on this thesis rests with the author and is made available under a Creative Commons Attribution Non-Commercial No Derivatives licence. Researchers are free to copy, distribute or transmit the thesis on the condition that they attribute it, that they do not use it for commercial purposes and that they do not alter, transform or build upon it. For any reuse or redistribution, researchers must make clear to others the licence terms of this work. 2 Dass ich erkenne, was die Welt Im Innersten zusammenh¨alt. Schau alle Wirkenskraft und Samen, Und tu nicht mehr in Worten kramen.1 Goethe, Faust There is much pleasure to be gained from useless knowledge. Bertrand Russell 1That I may detect the inmost force / Which binds the world, and guides its course; / Its germs, productive powers explore, / And rummage in empty words no more. Abstract Cold polar molecules provide unique opportunities to test fundamental physics and chemistry. Their permanent electric dipole moments and rich internal structure arising from their vibra- tional and rotational motion, makes them sensitive probes for new physics. These features also make them ideal for studying ultracold chemistry, for simulating the behaviour of strongly- interacting many-body quantum systems, and for quantum information science. This thesis describes a number of advances in cold molecule physics. The optimum method for producing an intense, pulsed, supersonic beam of cold CH molecules is investigated, result- ing in a beam with 3:5 × 109 ground state CH molecules per steradian per shot. The beam has a translational temperature of 400 mK and a velocity that is tuneable between 400 and 1800 m s−1. The lowest-lying Λ-doublet transitions of ground state CH, at 3:3 GHz and 0:7 GHz, are ex- ceptionally sensitive to variations in the fine-structure constant α and the electron-to-proton mass ratio µ. Many modern theories predict that these constants may depend on time, po- sition, or local matter density. Using a novel spectroscopic method, the frequencies of these microwave transitions are measured with accuracy down to 3 Hz. By comparing to radio- astronomical observations, the hypothesis that fundamental constants may differ between the high and low density environments of the Earth and the interstellar medium of the Milky Way is tested. These measurements find no variation and set upper limits of j∆α/αj < 2:1 × 10−7 and j∆µ/µj < 4:3 × 10−7. The frequency of the lowest millimetre-wave transition of CH, near 533 GHz, is also measured with an accuracy of 0:6 kHz. The development of a novel type of trap for ground-state polar molecules is presented. Trap- ping polar molecules is a necessary condition to cool them to ultracold temperatures of 1 µK and below. The trap uses a high intensity microwave field in a Fabry-P´erotresonator. Experimental and theoretical investigations are presented that explore the modes of the cavity, how to obtain the highest possible quality factor, and how to optimally couple the microwave power into the cavity. Finally, a cold supersonic beam of BH molecules is developed. This molecule appears to be particularly well-suited to direct laser cooling due to its favourable rotational structure and Franck-Condon factors. The laser cooling concept is described, and a first spectroscopic inves- tigation of the relevant molecular structure is presented. Acknowledgements I have been very fortunate to work with and learn from many people over the years and thank all of them. I want to express my deep gratitude to Mike for his advice and exceptional support and to Ed for giving me the opportunity to work in his group. Big thanks to Sean and Rich for showing me how stuff works and for your patience and support in the difficult times of molecular source witchcraft and systematic error hunting. Thanks for the great time in the lab, in the pub and in Bailey's. Credits to Ben for showing me how to deal with microwaves and to Jony for stimulating discussions and scanmaster. I am indebted to Jon and Steve for their great skills in finding creative solutions to my endless mechanical engineering challenges and to Val for solving some tricky riddles concerning electronics. Thanks to Sanja for her original admin skills and to Tony and Jon from the materials department for lending me their vector network analyzer. Cheers to the EDM, laser cooling and buffer gas crews for excellent discussions. I apologize for borrowing many of your things. Thanks to the rest of CCM for making my time here to such an enjoyable experience. Last but not least, a big thanks to Arnhilt, my friends and family for their fantastic support. 5 Contents Declaration of Authorship2 Abstract 4 Acknowledgements5 List of Figures 9 List of Tables 12 1 Introduction 13 1.1 Overview........................................ 14 1.2 The Atomic and Molecular Beam........................... 15 1.2.1 Motion is Heat................................. 15 1.2.2 Otto Stern - Of Spatial Quantisation and Bad Cigars........... 22 1.2.3 My Name is Rabi, I Have Come Here to Work............... 26 1.3 Why Cold Molecules?................................. 29 1.3.1 High Resolution Spectroscopy and Precision Measurements........ 30 1.3.2 Molecules and Time Reversal Symmetry................... 30 1.3.3 Do Enantiomers of Chiral Molecules have identical spectra?........ 34 1.3.4 Variation of Fundamental Constants..................... 34 1.3.5 Cold Chemistry................................. 37 1.3.6 Dipole Interactions and Quantum Gases of Polar Molecules........ 37 1.3.7 Quantum Simulation.............................. 38 1.3.8 Quantum Information............................. 40 1.4 How to Cool Molecules?................................ 40 1.5 Summary & Conclusion................................ 42 2 Molecular Physics - A Theoretical Description of the CH Molecule 44 2.1 Introduction....................................... 44 2.2 The Born-Oppenheimer Approximation....................... 45 2.3 The Rotational Structure of CH............................ 48 2.4 Transitions Between the Ground and Excited States................ 51 2.5 Stark Effect....................................... 55 2.6 Zeeman Effect...................................... 57 2.7 Summary........................................ 59 6 3 Experimental Setup and Molecular Sources 61 3.1 Introduction....................................... 61 3.2 The Vacuum System.................................. 62 3.3 Detection Hardware and Laser System........................ 64 3.3.1 The Transfer Cavity Lock........................... 68 3.3.2 The Detector.................................. 70 3.3.3 Detection Efficiency.............................. 72 3.4 The Ultimate Guide to Sources for the CH Molecule................ 76 3.4.1 How to Produce a Supersonic Beam of Diatomic Radicals......... 76 3.4.2 Supersonic Expansion............................. 80 3.4.3 Beams of CH molecules............................ 85 3.4.4 Source Hardware................................ 86 3.4.5 A Glow Discharge Source for Producing CH Molecules........... 87 3.4.6 A Discharge-Reaction Source for Producing CH Molecules......... 91 3.4.6.1 Determining the Flux........................ 96 3.4.7 Laser Ablation................................. 97 3.4.8 Photodissociation of Bromoform....................... 98 3.4.9 Valve Testing.................................. 104 3.4.10 Skimmer Interference............................. 108 3.4.10.1 Skimmer to Nozzle Distance.................... 108 3.5 Conclusion....................................... 110 4 Searching for Variations of Fundamental Constants Using CH Molecules 112 4.1 Introduction....................................... 112 4.2 How to Measure the Λ-doublet Transitions in CH?................. 120 4.2.1 Driving the Λ-doublet Transition with Microwaves - Theory........ 121 4.2.2 Experimental Setup.............................. 126 4.2.2.1 Transmission Line Resonator.................... 126 4.2.2.2 Controlling Magnetic Fields..................... 129 4.2.2.3 Microwave Electronics........................ 130 4.2.2.4 State Selector............................ 131 4.3 Measuring the J = 1=2 Λ-doublet........................... 132 4.3.1 First Preparations............................... 132 4.3.2 Measuring the J = 1=2 Λ-doublet Using Ramsey's Method of Separated Oscillatory Fields................................ 135 4.3.3 Systematic Frequency Shifts Related to Magnetic Fields.......... 137 4.3.4 Systematic Shifts Related to Electric Fields................. 139 4.3.5 Velocity Dependent Frequency Shifts..................... 139 4.3.6 Other Systematic Frequency Shifts...................... 142 4.3.7 Summary.................................... 144 4.4 Measuring the J = 3=2 Λ-doublet........................... 145 4.4.1 Systematic Shifts Related to Magnetic Fields................ 147 4.4.2 Systematic Shifts Related to Electric Fields................. 150 4.4.3 Velocity Dependent Frequency Shifts..................... 151 4.4.4 Other Systematic Effects........................... 151 4.4.5 Summary.................................... 152 4.5 Constraining