Rydberg molecules and circular Rydberg states in cold atom clouds by David Alexander Anderson A dissertation submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy (Applied Physics) in The University of Michigan 2015 Doctoral Committee: Professor Georg A. Raithel, Chair Professor Luming Duan Professor Alex Kuzmich Thomas Pohl, Max Plank Institute for Physics Associate Professor Vanessa Sih ⃝c David A. Anderson 2015 All Rights Reserved For my family ii ACKNOWLEDGEMENTS First I have to thank my advisor Georg Raithel for his continued support, patience, and encouragement during the completion of this dissertation and throughout my time working in the Raithel group. Without his insights, direction, and deep understanding of the subject matter, none of it would have been possible. His enthusiasm for research and insatiable curiosity have been an inspiration in the years I have been fortunate to have spent under his wing. Thank you Georg for giving me the opportunity to learn from you. Over the years I have had the pleasure of working with many former and current members of the Raithel group from whom I have learned a great deal. Many thanks to Sarah Anderson, Yun-Jhih Chen, Lu´ıs Felipe Gon¸calves, Cornelius Hempel, Jamie MacLennan, Stephanie Miller, Kaitlin Moore, Eric Paradis, Erik Power, Andira Ramos, Rachel Sapiro, Andrew Schwarzkopf, Nithiwadee Thaicharoen (Pound), Mallory Traxler, and Kelly Younge, for making my time in the Raithel group such an enjoyable experience. Thank you to my committee members, Georg Raithel, Thomas Pohl, Vanessa Sih, Alex Kuzmich, and Luming Duan, for your support and willingness to serve on my committee. Thank you Charles Sutton, Lauren Segall, Cynthia McNabb, and Cagliyan Kurdak in the Applied Physics Program and the staff in the Department of Physics here at the University of Michigan for all the wonderful work you do. This dissertation would not have been possible without the help and support of many other people. Thanks go to my fellow graduate students, Alex Toulouse, Liz Shtrahman, Chris Trowbridge, Channing Huntington, Prashant Padmanaban, Jeffrey Herbstman, An- drea Bianchini, Danny Maruyama, Mike McDonald, for your friendships and the adventures iii we have shared over the years. To my Brickhouse family: Alex, Liz (the summer sublet counts), Rob Wyman, Laurel Couture, Gina DiBraccio, Lucas Bartosiewicz, Haydee Iza- guirre, Cassandra Izaguirre, Megan Williams, Claire Roussel and Guilliaume Maisetti, Jenny Geiger, Sophie Kruz, Sarah Bliss, Carson Schultz, Megan Blair, and the many more friends and visitors that helped fill the house with great conversation and good company. Thank you for making Ann Arbor a place called home. Thank you Johnny Adamski and Nick Nacca for the fishing and camping trips, to Peter and Kathy Adamski for your love and support. And to my family, thank you for always pointing me in the right direction. iv TABLE OF CONTENTS DEDICATION :::::::::::::::::::::::::::::::::::::: ii ACKNOWLEDGEMENTS :::::::::::::::::::::::::::::: iii LIST OF FIGURES ::::::::::::::::::::::::::::::::::: viii LIST OF TABLES :::::::::::::::::::::::::::::::::::: xiv LIST OF APPENDICES :::::::::::::::::::::::::::::::: xv ABSTRACT ::::::::::::::::::::::::::::::::::::::: xvi CHAPTER I. Introduction .................................. 1 1.1 A historical perspective . 1 1.1.1 Long-range Rydberg molecules . 3 1.1.2 Circular Rydberg atoms . 6 1.2 Dissertation framework . 9 II. Theoretical background ........................... 10 2.1 Hydrogen . 10 2.2 Fine structure . 13 2.3 Rydberg atoms . 14 2.3.1 Radiative lifetimes . 16 2.3.2 Black body radiation . 18 2.3.3 Stark effect . 20 2.3.4 Rydberg excitation blockade . 22 2.4 Long-range Rydberg molecules . 23 2.4.1 Elastic scattering and partial waves . 23 2.4.2 Low-energy electron-Rb scattering . 25 2.4.3 Adiabatic molecular potentials and bound states . 30 2.4.4 Hund's coupling cases . 33 v III. Experimental methods ............................ 36 3.1 Preparation of cold rubidium ground-state atoms . 37 3.1.1 Laser cooling . 37 3.1.2 Magnetic trap and evaporative cooling . 39 3.1.3 Absorption imaging . 40 3.2 Rydberg excitation and detection . 41 3.3 Electric field control . 45 IV. Long-range D-type Rydberg molecules .................. 47 4.1 Experiment . 47 4.2 Molecular binding energies . 49 4.3 An S-wave Fermi model . 53 4.4 Transition between Hund's cases (a) and (c) . 56 4.5 Molecular line broadening . 59 4.6 Summary . 61 V. Angular-momentum couplings in long-range Rydberg molecules .. 63 5.1 The complete Fermi model . 64 5.2 Adiabatic molecular potentials . 67 5.3 Quasi-bound molecular states and lifetimes . 71 5.4 Hund's cases for nD Rydberg molecules revisited . 74 5.5 Electric and magnetic dipole moments . 77 5.6 Hyperfine-structure effects in deep 3S- and 3P-dominated potentials . 81 5.7 Summary . 82 VI. Production and trapping of cold circular Rydberg atoms ...... 84 6.1 Adiabatic crossed-fields method for circular state production . 86 6.2 Ground-state magnetic trap . 91 6.3 Production of circular states by the adiabatic crossed-fields method . 95 6.4 Circular-state trapping and center-of-mass oscillations . 99 6.5 Circular-state trap lifetime . 103 6.6 A model for collisions between circular Rydberg and ground-state atoms104 6.7 Internal-state evolution in a 300 K thermal radiation background . 110 6.8 Summary . 112 VII. Conclusion ................................... 114 APPENDICES :::::::::::::::::::::::::::::::::::::: 115 vi BIBLIOGRAPHY :::::::::::::::::::::::::::::::::::: 129 vii LIST OF FIGURES Figure 2.1 Calculated Veff of the electron-Rb polarization interaction for l = 0; 1; 2. 28 2.2 Calculated S-wave and P-wave phase shifts for low-energy electron-Rb scat- tering as a function of energy [1]. 29 87 2.3 Calculated S-wave adiabatic potential for the Rb(nD5=2 + 5S1=2) molecule with As0 = −14:0a0 and αRb = 319 a.u., and the ν = 0 vibrational wave function. 32 2.4 Vector angular-momentum coupling diagrams for Hund's cases (a), (b), and (c) with R =0. ................................. 34 3.1 Left: Schematic of the experimental apparatus [2]. Right: 87Rb hyperfine structure energy-level diagram. Frequency splittings, Land´eg-factors for each level and their corresponding Zeeman splitting between neighboring magnetic sub-levels are indicated on the plot. Values are taken from [3]. 38 3.2 Counter plots of jBj for three orthogonal planes through the center of the magnetic trap located 4 mm from the surface of the Z wire . Scale is 1 (blue) to 15 Gaus (red) in steps of 1 G; >15 G (hatched). 40 3.3 Left: Experimental chamber with the Z wire, counter-propagating 480nm and 780nm Rydberg excitation beams, and MCP are labeled. Six gold- coated copper electrodes (gray) enclose the trapped atom sample to control the electric fields in the experimental volume. The electrodes labeled \T" and \B" are used for field-ionization of Rydberg atoms and the electric-field ramp in circular state production (see Chapter VI), respectively. Right: 87Rb energy-level diagram for off-resonant two-photon excitation through intermediate 5P3=2 state. 43 3.4 Stark spectroscopy on 90D Rydberg states in rubidium: a) Calculated Stark map, b-d) Experimental Stark maps for electric fields generated along the X, Y, and Z coordinates. 46 viii 4.1 a) Schematic of the two-photon excitation to Rydberg and molecular states. The zoomed in region shows the 34D Rydberg fine structure (FS) states and their associated adiabatic S-wave molecular potentials. The binding energy Wν=0 of the ν = 0 vibrational molecular bound-state for each FS compo- nent is defined relative to the dissociation threshold equal to the respective Rydberg state energy, as labelled; (b) Schematic of the experimental timing sequence for Rydberg excitation, field-ionization and detection. 49 87 4.2 Spectrum centered on the 35D5=2 atomic Rydberg line showing the Rb(35D5=2+ 5S1=2)(ν = 0) molecular line at −38±3 MHz. The vertical error bars are the standard error of 3 sets of 55 individual experiments at each frequency step. The error in the binding energy is equal to the average long-term frequency drift observed over one full scan. 50 4.3 Right: Spectra centered on nD5=2 atomic Rydberg lines for the indicated values of n and identified molecular lines (squares). Left: Selected spectra from plot on right for states with identified molecular lines. Error bars are obtained as in Fig. 4.2. 51 4.4 (a) Binding energies obtained from Gaussian fits to the molecular lines iden- tified in Fig. 4.3 vs n. An allometric fit (solid curve) to the experimen- tal binding energies yields a n−5:9±0:4 scaling. Also shown are theoretical 87 binding energies for the Rb(nD5=2 + 5S1=2)(ν = 0) molecular states with As0=−14 a0 (hollow circles and dotted curve). (b) Peak number of detected ions on the nD5=2 atomic Rydberg line (solid diamonds, left axis) and ratio of molecular and atomic line strengths (hollow diamonds, right axis) vs n.. 52 4.5 (a) and (b): Deep (solid) and shallow (dashed) potentials for 35D3=2 and 35D5=2-type molecules, for As0 = −14 a0, and vibrational wave functions for ν = 0; 1 in the deep potentials. (c) and (d): Energy levels for ν = 0; 1 in the deep (triangles) and shallow (circles) potentials vs n............. 55 4.6 (a) ν = 0 binding energies in the deep molecular potentials for nD5=2 (filled triangles), nD3=2 (open triangles), and the D fine structure splitting (dashed line), vs effective quantum number. Solid lines are fits. The D3=2 energies 6:13 are fit well by 84.2 GHz/neff . The D5=2 energies do not exhibit a global 3:6 scaling; at low n they tend to scale as 23 MHz/neff . (b) Electric dipole moments for ν = 0 vs n for the deep (triangles) and shallow (circles) Vad(Z) for j = 3=2 (open) and j = 5=2 (filled).