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Quantum Reflection of Bose-Einstein Condensates Thomas A. Pasquini

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Quantum Reflection of Bose-Einstein Condensates Thomas A. Pasquini Quantum Reflection of Bose-Einstein Condensates by Thomas A. Pasquini B.A. Physics Dartmouth College, 2000 Submitted to the Department of Physics in partial fulfillment of the requirements for the degree of Doctor of Philosophy in Physics at the MASSACHUSETTS INSTITUTE OF TECHNOLOGY SEPTEMBER 2007 c Massachusetts Institute of Technology 2007. All rights reserved. Author............................................. ............................... Department of Physics August 21, 2007 Certified by......................................... ............................... Wolfgang Ketterle John D. MacAurthur Professor of Physics Thesis Supervisor Certified by......................................... ............................... David E. Pritchard Cecil and Ida Green Professor of Physics Thesis Supervisor Accepted by......................................... .............................. Thomas J. Greytak Professor of Physics, Associate Department Head for Education 2 Quantum Reflection of Bose-Einstein Condensates by Thomas A. Pasquini Submitted to the Department of Physics on August 21, 2007, in partial fulfillment of the requirements for the degree of Doctor of Philosophy in Physics Abstract Recent developments in atom optics have brought Bose-Einstein condensates within 1 µm of solid surfaces where the atom-surface interactions can no longer be ignored. At long- range, the atom-surface interaction is described by the weakly attractive Casimir-Polder potential which is classically predicted to accelerate an incident atom toward the surface where it will interact strongly with the internal modes of the surface, lose energy, and land in a bound state of the surface. When the incident atom is very cold, on the order of a few nanokelvin, however, the acceleration of the atomic wavefunction is so abrupt that the atom may partially reflect from the attractive tail in a process known as quantum reflection. This work presents experimental evidence for quantum reflection from a solid surface at normal incidence. Using atoms from a 23Na BEC, cooled to a few nanokelvin in a recently demonstrated single-coil trap, controlled collisions were induced between atoms and solid silicon surface. A maximum reflection probability of 12% was observed for an incident ∼ velocity of 1 mm/s. Atoms confined against the surface at low density exhibited an enhanced lifetime due to quantum reflection. A surprising aspect of quantum reflection is that nano-structured surfaces are predicted to exhibit enhanced quantum reflection due to the reduction of the atom-surface interaction from reduced density surfaces. Using a pillared surface with an density reduced to 1% of bulk density, we observe an enhancement of the reflection probability to 60%. ∼ At velocities from 2-25 mm/s, predicted threshold dependence of the reflection proba- bility was observed. At velocities below 2 mm/s, the reflection probability was observed to saturate. We develop a simple model which predicts the saturation as a result of mean-field interactions between atoms in the incident Bose-Einstein condensate. Thesis Supervisor: Wolfgang Ketterle Title: John D. MacAurthur Professor of Physics Thesis Supervisor: David E. Pritchard Title: Cecil and Ida Green Professor of Physics For the parents in my life, Sharon and Tom, Ann and Monty, and Elisabeth. Acknowledgments In 2002, I searched for a graduate research advisor who was excited about the “tabletop” research they were doing and who smiled in their photographs. With Dave and Wolfgang, I found excitement and smiles twice over. I thank them for the opportunity to explore and experiment in their lab for the last five years and for their support and encouragement throughout my time at MIT. Help exploring was never in short supply in the Science Chamber, and I have benefitted from group members who have moved on and those who will remain. My work here has been eased along by patience and understanding of graduate students Aaron and Yong, who nurtured my development on the apparatus, driven forward by the insights of post-docs Dave and Michele, and “boosted” by diploma students Andre, Christian, and Sebastian. Visitors to the group Won-Ho and Carsten have also contributed to the lab. Thank you for paving the way for this work. In recent years, we have all benefited greatly from the quiet diligence of Gyu-Boong, the gung-ho attitude of Caleb, the probing questions of Tony and the exuberance of Ye-Ryoung and Jae. Thank you for making the last years so productive and good luck in the years to come. The work of the Science Chamber is not limited to the members of BEC III. Up and down the building 26 hallway, collaborators in the Ketterle/Pritchard group and the Vuletic group too numerous to thank by name have left their mark on the experiments of the last 5 years. More recently, members of BEC I and BEC II, particularly Christian, Andre, Yong, Dan, and Jit Kee, have provided guidance and expertise in the rebuilding the Science Chamber to work with fermionic lithium. Beyond the halls of MIT, I have benefitted from discussions with Jim Babb and Robin Scott whose understanding of atom-surface potentials and BEC interactions have helped to grow and shape my own. Five years at MIT has shown me that even a competitive atmosphere can give rise to great friendships. I was fortunate, in my first years at MIT, to work with Jamil, Kendra, Julia, and Cort (and so many others) in an effort to secure health care funding for graduate students. That year I also fell in with Molly and Tim and Will and Sarah Jane who have remained close to my family throughout our time in Boston. Within the lab, there are too many friends to recognize individually. Four colleagues in particular, have been support in times of stress and joyful in times of success; thank you Micah, Gretchen, Jit Kee, and Dan for your friendship. Finally, the families at Westgate have made the last 6 months very special for my growing family; you are one of the greatest parts of MIT. Parents, to whom I have dedicated this work, have supported and encouraged me as I worked toward this degree. Tom and Sharon, my parents, believed in me and pushed me to do my best work throughout graduate school; thank you for your unswerving faith in me. Monty and Ann, my parents-in-law, are my family in Boston and have always opened their home to me, particularly following the birth of my children; thank you for all your support. Most importantly, my wife Elisabeth, now a parent herself, has carried me through the many challenges of MIT. I owe her so much, and I hope that the journey we begin now is the right path for our family. 8 Contents 1 Introduction: Nanokelvin Atoms and Surfaces 17 1.1 Phasetransitionsfordilutegases . ...... 18 1.2 Atomsnearsurfaces ............................... 20 1.2.1 The atom-atom interaction . 21 1.2.2 The atom-surface interaction . 24 1.3 BECIIIresearch ................................. 26 1.4 Outlineofthesis ................................. 26 2 The Science Chamber Apparatus 29 2.1 Apparatusoverview ............................... 29 2.1.1 23Na.................................... 30 2.1.2 Vacuumsystem.............................. 31 2.1.3 Coolingatoms .............................. 32 2.1.4 Magnetic and optical trapping . 34 2.1.5 Generationoflight ............................ 36 2.1.6 Imagingatoms .............................. 38 2.1.7 Thesciencechamber........................... 39 2.2 Thesingle-coiltrap.............................. 41 2.2.1 Single-loop trap geometry . 42 2.2.2 Sensitivity of the single-coil trap to external fields .......... 48 2.2.3 Experimental single-coil trap . 50 2.2.4 Further applications of the single-coil trap . ........ 53 2.3 Modifications for dual species work . ..... 53 2.3.1 Multi-speciesoven ............................ 54 2.3.2 Lithiumlasertable............................ 54 2.3.3 Large bias-field generation . 57 3 Quantum Reflection Theory 63 3.1 Quantum scattering from a 1-D potential . ..... 64 9 3.1.1 Barrierscattering. .. .. .. .. .. .. .. .. 65 3.1.2 Thresholdbehavior............................ 67 3.1.3 Numeric solutions for quantum reflection . 67 3.1.4 Thebadlandsfunction.......................... 67 3.2 Reflection of cold atoms from a solid surface . ....... 69 4 Normal Incidence Quantum Reflection 73 4.1 Previous work on quantum reflection . 73 4.2 History of quantum reflection experiments at MIT . ....... 75 4.3 Reflectionatnormalincidence. 78 4.4 Experimentalresults .. .. .. .. .. .. .. .. 79 4.4.1 Reflectionprobability . 80 4.4.2 Quantum reflection surface trap . 80 5 Structured Potentials for Quantum Reflection 83 5.1 Candidates for improved reflection . ..... 84 5.1.1 Silicaaerogels............................... 84 5.1.2 Periodically pillared surfaces . 85 5.1.3 Laserablatedsurfaces . 87 5.1.4 Carbonfilms ............................... 87 5.1.5 Piezo-modulated silicon . 87 5.2 What potential does an atom see? . 88 5.2.1 Modelsofthepillaredsurface . 88 5.2.2 Spuriousinteractions. 93 5.3 Experimentalresults .. .. .. .. .. .. .. .. 94 5.3.1 Reflectionprobability . 95 6 Interaction Effects in Quantum Reflection 97 6.1 Thefailureofsimplemodels. 97 6.2 An improved model for mean-field effects . 98 6.3 Experimentalresults .. .. .. .. .. .. .. .. 100 6.3.1 Reflectionprobability . 100 6.3.2 Excitations during reflection . 101 7 Conclusion 105 7.1 Applications of quantum reflection . 105 7.1.1 Focusingatomicbeams . .. .. .. .. .. .. .. 105 7.1.2 Trapping of ultracold atoms . 106 7.1.3 Fundamental condensate physics . 107 10 7.2 ThefutureoftheScienceChamber . 107 A Cooling Bose-Einstein
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