Probing Correlated Quantum Many-Body Systems at the Single-Particle Level PDF
Preview Probing Correlated Quantum Many-Body Systems at the Single-Particle Level
Springer Theses Recognizing Outstanding Ph.D. Research Manuel Endres Probing Correlated Quantum Many-Body Systems at the Single-Particle Level 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. Manuel Endres Probing Correlated Quantum Many-Body Systems at the Single-Particle Level Doctoral Thesis accepted by Ludwig Maximilian University of Munich, Germany 123 Author Supervisor Dr. Manuel Endres Prof.Immanuel Bloch Max-Planck-lnstitute ofQuantum Optics Max-Planck-lnstitute ofQuantum Optics Garching Garching Germany Germany ISSN 2190-5053 ISSN 2190-5061 (electronic) ISBN 978-3-319-05752-1 ISBN 978-3-319-05753-8 (eBook) DOI 10.1007/978-3-319-05753-8 Springer ChamHeidelberg New YorkDordrecht London LibraryofCongressControlNumber:2014936453 (cid:2)SpringerInternationalPublishingSwitzerland2014 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 theCopyright Law of the Publisher’s location, in its current version, and permission for use must always be obtained from Springer. Permissions for use may be obtained through RightsLink at the CopyrightClearanceCenter.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) Supervisor’s Foreword Ultracold atoms and molecules offer unique possibilities for probing strongly correlatedquantummany-bodyphasesinahighlycontrolledenvironment.Sofar, most of the analyses of cold atomic gases have relied on time-of-flight images, where the gas is released from the trap and its momentum distribution measured, or on low-resolution photographs taken of the gases in the trap. The thesis of Manuel Endres shows how such detection capabilities can be dramatically enhancedbybeingabletoobserveindividualatomsinthegasviahigh-resolution fluorescence imaging. This truly marks another revolution in the field of cold quantum gases! Now it is not only possible to image the average density distri- bution with high resolution, but to also directly detect all particle fluctuations in thesystem.Itisworthwhilerememberingthatthefluctuationsinaquantumsystem and the full underlying distribution functions fully characterize the properties of thesystem—farbeyondwhatwecanlearnfromsimpleexpectationvaluesoflocal observables.Byusingthisnovelimagingtechnique,ManuelEndreshasbeenable to directly measure correlation functions for quantum many-body systems that have never been accessible before, but play a crucial role in characterizing the ‘hidden’ order present in many correlated quantum systems. AnotherremarkableachievementinManuelEndres’thesisistheobservationof theHiggsmodeinatwo-dimensionalsuperfluid.Theexistenceofsuchamodein low-dimensionalsuperfluidshasbeendebatedforalongtime.Severalpapershave argued thatthe decay of‘Higgs’ excitations into Goldstone modes will lead toan overdamped response. More recent theory has argued that this should not be the case if a response to the absolute value of the order parameter is measured. With theexperimentspresentedinthisthesis,Manuelhasshownhowthisdebatecanbe settled toa large degree by using asuperfluidcloseto aquantumphase transition toa Mottinsulating state ofmatter. Close to such aquantumphase transition, the orderparameter—thecondensatewavefunction—acquiresarelativisticdynamical behaviour, just as the one that emerges from the most basic relativistic quantum field theories. His work gives an excellent pedagogical introduction to the timely subjectofHiggsparticlesandtheAnderson–Higgsmechanismandshowshowthe former can be measured using cold atomic quantum gases. This is a remarkable achievementandconnectsphysicsatthelowestenergyscalesinthemicro-Kelvin regime to the one of relativistic quantum field theories typically analysed at 23 v vi Supervisor’sForeword ordersofmagnitudehigherenergiesinhigh-energyphysicsexperiments!Manuel’s thesis has thereby opened new directions for quantum simulations with ultracold atoms beyond condensed matter and statistical physics applications. What singles out this thesis—besides the outstanding scientific results—is its style ofpresentation. Inavery clear andpedagogical manner, complexandwide- ranging physics topics are introduced tothe reader. Ihopeyou will enjoy reading thiseditedformofthethesisasmuchasIhaveandthatyouwillbeinspiredbyits content and presentation for your own scientific work. Munich, March 2014 Prof. Immanuel Bloch Abstract The detection of correlation and response functions plays a crucial role in the experimental characterization of quantum many-body systems. In this thesis, we present novel techniques for the measurement of such functions at the single- particle level. Specifically, we show the single-atom and single-site-resolved detection of an ultracold quantum gas in an optical lattice. The quantum gas is described by the Bose–Hubbard model, which features a zero temperature phase transition from a superfluid to a Mott insulating state, a paradigm example of a quantum phase transition. We used the aforementioned detection techniques to study correlation and response properties across the superfluid-Mott insulator transition. Thesingle-atomsensitivityofourmethodisachievedbyfluorescencedetection of individual atoms with a high signal-to-noise ratio. A high-resolution objective collects the fluorescence light and yields in situ ‘‘snapshots’’ of the quantum gas that allow for a single-site-resolved reconstruction of the atomic distribution. This allowed us to measure two-site and nonlocal correlation functions across the superfluid-Mott insulator transition. Nonlocal correlation functions are based on the information about an extended region of the system and play an important role in the characterization of low-dimensional quantum phases. While nonlocal correlation functions were so far only theoretical tools, our results show that they are actually experimentally accessible. Furthermore, we used a new thermometry scheme, based on the counting of individual thermal excitations, to measure the response of the system to lattice modulation. Using this method, we studied the excitation spectrum of the system across the two-dimensional superfluid-Mott insulator transition. In particular, we detecteda‘‘Higgs’’amplitudemodeinthestronglyinteractingsuperfluidcloseto the transition point where the system is described by an effectively Lorentz invariant low-energy theory. Our experimental results helped to resolve a debate about the observability of Higgs modes in two-dimensional systems. vii Acknowledgments IcannotthankImmanuelBlochenough forhissupportduringthelastyears.Iam particularly grateful that he always took his time despite his full schedule, was always open to new ideas and created an excellent scientific environment that he keeps on building. IamnolessindebtedtoStefanKuhrwhoseguidancewassocrucialformeand the whole Single Atoms team. It was a real pleasure to learn physics from him, about presenting results, and about all the technical things in the lab for which I believe there is no better teacher out there. IwouldliketothankallthecurrentandpreviousmembersoftheSingleAtoms team.Ibelieveoursuccesswas,firstandforemost,aresultofgreatteamwork!For somanyreasons,someofwhichIamstatingexplicitly,Iamparticularlygratefulto JacobSherson,forbeingagreatmentorinthefirstyearsandforthefunwehad together, inside and outside the lab; ChristofWeitenberg,forbeingagreatPh.D.comrade,forsomanymemorable hours we spent in the lab together, and for his enormous sense of humour; Takeshi Fukuhara, for being such a great help during the particle-hole and the Higgs project, and for the selfless general support; MarcCheneau,forallthehelpduringthelastyears,inparticular,forhelpingto get the experiment stable; PeterSchauß,forallthesupportanddiscussionsinthelast2yearsofthethesis, in particular for all the programming and for proofreading the whole thesis; Christian Gross, Johannes Zeiher and Sebastian Hild, who joined the Single Atoms team during the later stages of my thesis, and who helped a lot through discussions and by proofreading the thesis. Many of our projects were experiment–theory collaborations and I would like tothankourtheorycollaboratorsfortheirworkandforteachingmeagreatdealof physics. I would particularly like to thank Leonardo Mazza, David Pekker, Lode Pollet,MariCarmenBañuls,EugeneDemler,SteffenRathandWilhelmZwerger. In some cases, the initial trigger for an experiment or a crucial piece of advice camefrompeoplewhodonotappearasauthorsonourpublications.Inparticular, the interaction with Ehud Altman, Emanuele Dalla Torre, Daniel Podolski, Subir Sachdev, Nikolay Prokov’ev and Ignacio Cirac was absolutely crucial. Myspecialthanksalsogotocertainnon-scientificcolleagues,whohelpedwith organizational and technical support, in particular, Marianna Kargl, Ildiko ix x Acknowledgments Kecskesi, Zohra Hauck, Christine Best, Karsten Förster, Markus Böhm, Michael Pruscha,HeinzLenkandallthosewhokeepthePhysicsDepartmentinMainzand the Max-Planck-Institute of Quantum Optics running and make them outstanding places for science. Furthermore, I would like to thank all other members of the BlochgroupwhohelpedandsupportedmeduringmyPh.D.,especiallySebastian Will, Ulrich Schneider, Simon Braun, Dries van Osten and Stefan Trotzky. My best friends Hausi, Knödel and Anne should know how thankful I am for their friendship and support. My parents, Eugen and Luitgard, and my brother Gerald have always been there for me in the most selfless manner, particularly, during the time ofmyPh.D. Last butnotleast, Iwould liketothankTracy for so manythingsforwhichthereisnotenoughspacehere,particularlyforthesupport duringtheintensephasesofmyPh.D.,whenIwasnotsoeasytocomealongwith, and for proofreading my German English.
The list of books you might like
