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Laser Cooling and Slowing of a Diatomic Molecule John F Abstract Laser cooling and slowing of a diatomic molecule John F. Barry 2013 Laser cooling and trapping are central to modern atomic physics. It has been roughly three decades since laser cooling techniques produced ultracold atoms, leading to rapid advances in a vast array of fields and a number of Nobel prizes. Prior to the work presented in this thesis, laser cooling had not yet been extended to molecules because of their complex internal structure. However, this complex- ity makes molecules potentially useful for a wide range of applications. The first direct laser cooling of a molecule and further results we present here provide a new route to ultracold temperatures for molecules. In particular, these methods bridge the gap between ultracold temperatures and the approximately 1 kelvin temperatures attainable with directly cooled molecules (e.g. with cryogenic buffer gas cooling or decelerated supersonic beams). Using the carefully chosen molecule strontium monofluoride (SrF), decays to unwanted vibrational states are suppressed. Driving a transition with rotational quantum number R=1 to an excited state with R0=0 eliminates decays to unwanted ro- tational states. The dark ground-state Zeeman sublevels present in this specific scheme are remixed via a static magnetic field. Using three lasers for this scheme, a given molecule should undergo an average of approximately 100; 000 photon absorption/emission cycles before being lost via un- wanted decays. This number of cycles should be sufficient to load a magneto-optical trap (MOT) of molecules. In this thesis, we demonstrate transverse cooling of an SrF beam, in both Doppler and a Sisyphus-type cooling regimes. We also realize longitudinal slowing of an SrF beam. Finally, we detail current progress towards trapping SrF in a MOT. Ultimately, this technique should enable the production of large samples of molecules at ultracold temperatures for molecules chemically distinct from competing methods. Laser cooling and slowing of a diatomic molecule A Dissertation Presented to the Faculty of the Graduate School of Yale University in Candidacy for the Degree of Doctor of Philosophy by John F. Barry Dissertation Director: David DeMille December 2013 Copyright c 2013 by John F. Barry All rights reserved. 2 Contents 1 Introduction 6 1.1 Why cold polar molecules? ................................ 7 1.2 Production methods for cold and ultracold molecules .................. 8 1.3 Direct laser cooling of a diatomic molecule ........................ 11 1.3.1 A cycling transition for a diatomic molecule . 12 1.4 Thesis organization ..................................... 12 2 Molecules and SrF 14 2.1 Energy level overview ................................... 15 2.2 Electronic energy levels .................................. 16 2.3 Vibrational energy levels .................................. 18 2.4 Rotational energy levels .................................. 18 2.4.1 The Dunham model ................................ 19 2.5 Fine structure, hyperfine structure, spin-rotation, and Lambda-doubling energy levels 22 2.5.1 X state spin-rotation and hyperfine structure . 22 2.5.2 A state spin-orbit and Lambda-doubling structure . 25 2.6 Labeling of transitions ................................... 27 2.7 Coupling of angular momenta ............................... 30 2.8 Franck-Condon factors ................................... 31 2.9 Branching ratios ...................................... 33 2.9.1 Calculation overview ................................ 33 2.10 Energy shifts in the presence of an external magnetic field . 35 2.11 Exact electronic ground state Hamiltonian ........................ 37 3 3 SrF and cycling 39 3.1 Quasi-cycling transition .................................. 39 3.1.1 Vibrational branching ............................... 39 3.1.2 Rotational branching ................................ 41 3.1.3 Dark states ..................................... 42 3.1.4 Addressing spin-rotational and hyperfine structure . 44 3.2 Simplified models of our system .............................. 46 3.3 Absorption cross section, saturation intensity, etc. ................... 48 3.3.1 Rabi frequency ................................... 49 3.3.2 Absorption cross section without broadening . 51 3.3.3 Multilevel rate equations ............................. 51 3.3.4 Multilevel rate equation example ......................... 52 3.3.5 Multilevel rate equations applied to SrF ..................... 54 3.4 Optical Bloch equations .................................. 60 3.4.1 Solving the OBEs ................................. 60 3.4.2 OBE results ..................................... 62 3.4.3 (3,3)+1 system ................................... 62 3.4.4 (2,4)+2 system ................................... 64 3.5 Loss mechanisms ...................................... 67 3.6 Benefits of SrF ....................................... 70 3.6.1 Drawbacks of SrF ................................. 72 4 The laser system 73 4.1 Introduction ......................................... 73 4.2 External cavity diode lasers ................................ 73 4.2.1 Pivot point calculations .............................. 76 4.3 Electro-optic modulators .................................. 78 4.3.1 Simple phase modulation theory ......................... 78 4.3.2 Construction and components ........................... 80 4.3.3 Current problems .................................. 81 4.4 Laser amplifiers ....................................... 82 4.4.1 Injection-seeded slave ............................... 82 4 4.4.2 Tapered amplifier.................................. 84 4.4.3 Tapered amplifier setup and alignment...................... 87 4.4.4 Tapered amplifier protection circuit ....................... 91 4.4.5 Additional TA experiences ............................. 91 4.5 Fabry-P´erot ......................................... 93 4.6 Frequency reference .................................... 99 4.7 Software lock ........................................ 100 4.7.1 Scanning ...................................... 101 5 A bright, slow cryogenic molecular beam source for free radicals 105 5.1 Introduction ......................................... 105 5.2 General source properties ................................. 107 5.2.1 Mean free path ................................... 108 5.2.2 Thermalization ................................... 110 5.2.3 Diffusion and extraction .............................. 111 5.2.4 Beam formation .................................. 112 5.3 Experimental apparatus .................................. 113 5.4 Experimental results .................................... 117 5.4.1 In-cell dynamics and SrF properties . 117 5.4.2 Molecular beam properties ............................ 121 5.5 Subsequent source improvements ............................. 131 6 Radiative force from optical cycling on a diatomic molecule 133 6.1 Introduction ......................................... 133 6.2 Experimental considerations for deflection . 134 6.3 Experimental apparatus .................................. 134 6.4 Results ............................................ 137 7 Laser cooling of a diatomic molecule 140 7.1 Experimental apparatus .................................. 140 7.2 Results overview ...................................... 142 7.3 Quantitative analysis .................................... 149 7.3.1 Capture velocity and optimum magnetic field for Sisyphus and Doppler forces 149 5 7.3.2 Estimation of temperature ............................. 151 7.3.3 Power dependence of Sisyphus and Doppler cooling . 154 7.4 Chapter conclusion ..................................... 155 8 Laser radiation pressure slowing of a molecular beam 156 8.1 Introduction ......................................... 156 8.2 Experimental apparatus .................................. 157 8.3 Results ............................................ 160 9 Progress towards a 3-D MOT 165 9.1 An SrF MOT ........................................ 165 9.1.1 Non-traditional MOTS ............................... 165 9.1.2 MOT polarization ................................. 166 9.1.3 Unintended excitation ............................... 166 9.1.4 Preliminary MOT design ............................. 168 9.2 Frequency distribution of slowing light . 169 9.3 Vacuum system ....................................... 172 9.3.1 Beam attenuation by room temperature gases . 172 9.3.2 Calculating gas loads and partial pressures . 174 9.3.3 Pumping of helium gas ............................... 175 9.3.4 Revisions to vacuum system ............................ 176 9.4 Simultaneous cooling and slowing ............................. 178 9.4.1 Experimental apparatus .............................. 179 9.4.2 Experimental results ................................ 180 9.5 MOT detection ....................................... 182 9.5.1 Ion detection .................................... 184 9.5.2 Blue detection ................................... 187 9.5.3 Current detection .................................. 187 9.5.4 Light collection ................................... 189 9.5.5 Scattered light ................................... 190 10 Outlook and future directions 194 10.1 Non-radiative slowing ................................... 194 6 10.1.1 Transverse confinement methods . 194 10.2 Collisions and chemical reactions ............................. 195 10.3 Leaky MOT ......................................... 196 10.4 Cooling beyond MOT temperatures . 196 10.5 Trapped fluorine ...................................... 197 APPENDICES 198 A Franck-Condon
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