Springer Theses Recognizing Outstanding Ph.D. Research For furthervolumes: http://www.springer.com/series/8790 Aims and Scope The series ‘‘Springer Theses’’ brings together a selection of the very best Ph.D. theses from around the world and across the physical sciences. Nominated and endorsed by two recognized specialists, each published volume has been selected for its scientific excellence and the high impact of its contents for the pertinent fieldofresearch.Forgreateraccessibilitytonon-specialists,thepublishedversions includeanextendedintroduction,aswellasaforewordbythestudent’ssupervisor explaining the special relevance of the work for the field. As a whole, the series will provide a valuable resource both for newcomers to the research fields described, and for other scientists seeking detailed background information on specialquestions.Finally,itprovidesanaccrediteddocumentationofthevaluable contributions made by today’s younger generation of scientists. Theses are accepted into the series by invited nomination only and must fulfill all of the following criteria • They must be written in good English. • ThetopicshouldfallwithintheconfinesofChemistry,Physics,EarthSciences, Engineering andrelatedinterdisciplinaryfieldssuchasMaterials, Nanoscience, Chemical Engineering, Complex Systems and Biophysics. • The work reported in the thesis must represent a significant scientific advance. • Ifthethesisincludespreviouslypublishedmaterial,permissiontoreproducethis must be gained from the respective copyright holder. • They must have been examined and passed during the 12 months prior to nomination. • Each thesis should include a foreword by the supervisor outlining the signifi- cance of its content. • The theses should have a clearly defined structure including an introduction accessible to scientists not expert in that particular field. Tongcang Li Fundamental Tests of Physics with Optically Trapped Microspheres Doctoral Thesis accepted by the University of Texas at Austin, USA 123 Author Supervisor Dr. TongcangLi Prof.Dr. MarkG.Raizen NSFNanoscale Science Center forNonlinear Dynamics and EngineeringCenter and Department ofPhysics Universityof California Universityof Texasat Austin Berkeley,CA Austin, TX USA USA ISSN 2190-5053 ISSN 2190-5061 (electronic) ISBN 978-1-4614-6030-5 ISBN 978-1-4614-6031-2 (eBook) DOI 10.1007/978-1-4614-6031-2 SpringerNewYorkHeidelbergDordrechtLondon LibraryofCongressControlNumber:2012950387 (cid:2)SpringerScience+BusinessMediaNewYork2013 Thisworkissubjecttocopyright.AllrightsarereservedbythePublisher,whetherthewholeorpartof the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation,broadcasting,reproductiononmicrofilmsorinanyotherphysicalway,andtransmissionor informationstorageandretrieval,electronicadaptation,computersoftware,orbysimilarordissimilar methodology now known or hereafter developed. Exempted from this legal reservation are brief excerpts in connection with reviews or scholarly analysis or material supplied specifically for the purposeofbeingenteredandexecutedonacomputersystem,forexclusiveusebythepurchaserofthe work. Duplication of this publication or parts thereof is permitted only under the provisions of theCopyrightLawofthePublisher’slocation,initscurrentversion,andpermissionforusemustalways beobtainedfromSpringer.PermissionsforusemaybeobtainedthroughRightsLinkattheCopyright ClearanceCenter.ViolationsareliabletoprosecutionundertherespectiveCopyrightLaw. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publicationdoesnotimply,evenintheabsenceofaspecificstatement,thatsuchnamesareexempt fromtherelevantprotectivelawsandregulationsandthereforefreeforgeneraluse. While the advice and information in this book are believed to be true and accurate at the date of publication,neithertheauthorsnortheeditorsnorthepublishercanacceptanylegalresponsibilityfor anyerrorsoromissionsthatmaybemade.Thepublishermakesnowarranty,expressorimplied,with respecttothematerialcontainedherein. Printedonacid-freepaper SpringerispartofSpringerScience+BusinessMedia(www.springer.com) Dedicated to my parents, Daogan Li and Zhangman Huang, my wife, Ruyi Li, and my sister, Xiaoping Li, for their endless love and support Supervisor’s Foreword I am very pleased to introduce this Ph.D. Thesis by Dr. Tongcang Li. Tongcang was a graduate student under my supervision, and completed his Ph.D. in May 2011. He was the senior student on anexperiment tostudy the motionof micron- sizedbeadsofglassheldinopticaltweezers.Thissystemhasprovidedspectacular experimentalresults,andIcreditTongcangwiththevisionandtheabilitytopullit off. We were able to resolve, for the first time, the instantaneous velocity of a Brownian particle in air. In 1907, Albert Einstein analyzed this problem and showed that such a measurement could be used to test the energy equipartition theorem, one of the basic tenets of statistical mechanics. However, Einstein concludedinhispaperthatthetime-scalewastooshorttobemeasuredinpractice! This prediction held for over 100 years, but Tongcang Li was able to meet the challenge of Albert Einstein, and to measure the instantaneous velocity of a Brownian particle. We used the velocity data to verify directly the energy equi- partitiontheoremforaBrownianparticle.Theworkhasattractedgreatinterestand press, partly due to the historical challenge by Einstein, and also because it addresses fundamental questions on statistical mechanics of small systems. Following that work, Tongcang led an experiment to cool the center-of-mass motion of a bead in vacuum close to the absolute zero of temperature. This looks like an ideal system to test quantum mechanics at the boundary between the microscopic and macroscopic, and answer fundamental questions about the col- lapse of the wave function due to the environment. Inparallel,Tongcangstartedoureffortstoobservetheinstantaneousvelocityof abeadinwater,andweexpecttobeabletocompletethisworkinthenearfuture. I believe that this experiment will serve as a new testing ground for statistical mechanics on short time scales. It will also be a new probe into the nature of complex fluids, such as water, a topic of great interest to chemists and biologists. Inrecognitionoftheseaccomplishments,TongcangwasawardedaBiedenharn Graduate Fellowship in the physics department. He also won the Jean Bennett Memorial Student Travel Grant from the Optical Society of America Foundation (the only one out of 80 applicants), and the Chinese Government Award for vii viii Supervisor’sForeword Outstanding Self-financed Students Abroad. Tongcang was recognized by the UT Physics Department outstanding Ph.D. award. In summary, this Ph.D. Thesis by Tongcang Li is simply outstanding, and is a worthy addition to the Springer Thesis Series. Austin, August 2012 Prof. Dr. Mark Raizen Acknowledgments First,Iwouldliketothankmysupervisor,Dr.MarkRaizen,forprovidingmethe opportunitytoworkinanoutstanding group. Markis agreatpersontoworkwith and is full of ideas. I am impressed by his vision and confidence. Mark often proposesambitiousideasthatmayappearsuspicioustomostpeopleatfirst.During mytimeinhisgroup,Ihadtheprivilegetowitnesstheseideasultimatelyrealized in ground-breaking experiments. I could not have asked for a better advisor to learn how to do creative research. I joined the lab in November 2004 to work on the sodium Bose–Einstein condensate (BEC) experiment with Kevin Henderson and Hrishikesh Kelkar. Kevin was very helpful and excellent in teaching. I learned a lot of experimental skills from him, including driving a car. Hrishi was extremely patient and hard working. He aligned a lot of difficult parts of the optics, some of which took severalweeksofcontinuouswork.DavidMedellinjoinedthisexperimentin2006. David is fantastic with mathematics and physical concepts, which is very helpful toourwork.Heisalwaystryinghisbesttomakehisworkperfect. Ialsoenjoyed the dinners with Hrishi and David when we were working together. Kirsten VieringjoinedthisexperimentasaWürzburgexchangestudentandlaterreturned backafterworkingonaRubidiumexperiment.Sheisaverygoodexperimentalist and works very efficiently. I started the new experiment on optical trapping and cooling of microspheres with the help of David Medellin. A particular thanks goes to Simon Kheifets. He joinedthisexperimentjustafterwewereabletotrapmicrospheresinvacuumand has participated in almost all aspects of this experiment since then. He worked very hard and helped me to make this experiment fruitful. I also enjoyed the discussionswithhimonournewideasalmosteveryday.Ifullyexpectthathewill push the experiment to an unprecedented level. I would also like to thank Ivo Popov, Ioannis K. Charidakos, and Isaac Chavez for their contributions to this experiment. Iwouldliketothankotherstudentsinthelabwhohaveprovidedmuchhelpto me.TheyareBraulioGutierrez-Medina,ToddMeyrath,Chih-SungChuu,Gabriel Price, Travis Bannerman, Ed Narevicius, Adam Libson, Rob Clark, Tom Mazur, ix x Acknowledgments Melissa Jenkins, and Jianyong Mo. I would also like to thank Charlotte Sanders, Francisco Camargo, Daniel Ellsworth, Julia Majors, Christoph Schaeff, Christian Parthey, Max F. Riedel, Artem M. Dudarev, Chuanwei Zhang, and Shoupu Wan for making the environment of our lab friendly and enjoyable. IwouldliketothankJackClifford,AllanSchroederandallothermembersofthe machineshop,andEd Baez andLarrySandefurinthe cryo labfor their excellent work.IwouldliketothankOlgaVera,ElenaSimmons,MarybethCasias,andother membersof CNLD for their administrative help. I also appreciate the friendships of Shaoping Lu, Hui Chen, Ning Kong, Huai Huang, Jiaxin Han, Tianyi Yang, Zhangqi Yin, Ming Lei, Kin Chung Fong, and more. Finally, I would definitely like to thank my wife, Ruyi Li. She is very sup- portive and provides me a sweet home. I also want to thank my parents and my sister for their endless love and encouragement. 28 April 2011, Austin, TX, USA Tongcang Li Contents 1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.1 Macroscopic Quantum Mechanics. . . . . . . . . . . . . . . . . . . . . . 1 1.2 Instantaneous Velocity of Brownian Motion. . . . . . . . . . . . . . . 3 1.3 Contents of this Dissertation. . . . . . . . . . . . . . . . . . . . . . . . . . 5 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 2 Physical Principle of Optical Tweezers. . . . . . . . . . . . . . . . . . . . . 9 2.1 Ray Optics Approximation. . . . . . . . . . . . . . . . . . . . . . . . . . . 10 2.2 Rayleigh Approximation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 2.3 Generalized Lorentz-Mie Theory. . . . . . . . . . . . . . . . . . . . . . . 15 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 3 Optical Trapping of Glass Microspheres in Air and Vacuum. . . . . 21 3.1 Launching Microspheres. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22 3.2 Trapping Microspheres. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27 3.2.1 Optical Levitation Trap . . . . . . . . . . . . . . . . . . . . . . . . 28 3.2.2 Counter-Propagating Dual-Beam Optical Trap . . . . . . . . 30 3.3 Vacuum System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37 4 Measuring the Instantaneous Velocity of a Brownian Particle in Air. . . . . . . . . . . . . . . . . . . . . . . . . . . . 39 4.1 Theories of Brownian Motion. . . . . . . . . . . . . . . . . . . . . . . . . 39 4.1.1 A Free Particle. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39 4.1.2 A Trapped Microsphere. . . . . . . . . . . . . . . . . . . . . . . . 41 4.2 A Fast Detection System . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46 4.3 Measured Power Spectra . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47 4.4 Measurement of the Instantaneous Velocity of a Brownian Particle in Air . . . . . . . . . . . . . . . . . . . . . . . . . 50 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57 xi