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Undergraduate Texts in Physics Ray LaPierre Getting Started in Quantum Optics Undergraduate Texts in Physics SeriesEditors KurtH.Becker,NYUPolytechnicSchoolofEngineering,Brooklyn,NY,USA Jean-MarcDiMeglio,MatièreetSystèmesComplexes,UniversitéParisDiderot, BâtimentCondorcet,Paris,France SadriD.Hassani,UniversityofIllinoisatUrbana-Champaign,Urbana,IL,USA MortenHjorth-Jensen,UniversityofOslo,Oslo,Norway MichaelInglis,Patchogue,NY,USA BillMunro,NTTBasicResearchLaboratories,OpticalScienceLaboratories, Atsugi,Kanagawa,Japan SusanScott,AustralianNationalUniversity,Acton,ACT,Australia MartinStutzmann,WalterSchottkyInstitute,TechnicalUniversityofMunich, Garching,Bayern,Germany UndergraduateTextsinPhysics(UTP)publishesauthoritativetextscoveringtopics encounteredinaphysicsundergraduatesyllabus.Eachtitleintheseriesissuitableas an adopted text for undergraduate courses, typically containing practice problems, worked examples, chapter summaries, and suggestions for further reading. UTP titles should provide an exceptionally clear and concise treatment of a subject at undergraduatelevel,usuallybasedonasuccessfullecturecourse.Coreandelective subjectsareconsideredforinclusioninUTP. UTPbookswillbeidealcandidatesforcourseadoption,providinglecturerswith a firm basis for development of lecture series, and students with an essential referencefortheirstudiesandbeyond. Ray LaPierre Getting Started in Quantum Optics RayLaPierre Hamilton,ON,Canada ISSN2510-411X ISSN2510-4128 (electronic) UndergraduateTextsinPhysics ISBN978-3-031-12434-1 ISBN978-3-031-12432-7 (eBook) https://doi.org/10.1007/978-3-031-12432-7 ©TheEditor(s)(ifapplicable)andTheAuthor(s),underexclusivelicensetoSpringerNatureSwitzerland AG2022 Thisworkissubjecttocopyright.AllrightsaresolelyandexclusivelylicensedbythePublisher,whether thewholeorpartofthematerialisconcerned,specificallytherightsoftranslation,reprinting,reuseof illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similarordissimilarmethodologynowknownorhereafterdeveloped. Theuseofgeneraldescriptivenames,registerednames,trademarks,servicemarks,etc.inthispublication doesnotimply,evenintheabsenceofaspecificstatement,thatsuchnamesareexemptfromtherelevant protectivelawsandregulationsandthereforefreeforgeneraluse. The publisher, the authors, and the editorsare safeto assume that the adviceand informationin this bookarebelievedtobetrueandaccurateatthedateofpublication.Neitherthepublishernortheauthorsor theeditorsgiveawarranty,expressedorimplied,withrespecttothematerialcontainedhereinorforany errorsoromissionsthatmayhavebeenmade.Thepublisherremainsneutralwithregardtojurisdictional claimsinpublishedmapsandinstitutionalaffiliations. ThisSpringerimprintispublishedbytheregisteredcompanySpringerNatureSwitzerlandAG Theregisteredcompanyaddressis:Gewerbestrasse11,6330Cham,Switzerland Preface Getting Started in Quantum Optics was born from lecture notes developed for an introductory course in quantum optics offered to undergraduate students in the Department of Engineering Physics at McMaster University (Hamilton, Ontario, Canada). The book was written for students who have completed an introductory course on quantum mechanics and electromagnetism, but otherwise have no back- groundinquantumoptics.GettingStartedinQuantumOpticsismostlyintendedasa self-contained introduction to the theory of quantum optics with the beginner inmind. This book covers canonical quantization, the quantumharmonic oscillator, vac- uumfluctuations,Fockstates,thesinglephotonstate,thequantumopticstreatment ofthebeamsplitterandtheinterferometer,multimodequantizedlight,andcoherent andincoherentstates.Thebookprovidesatreatmentofsqueezedlightanditsusein the Laser Interferometer Gravitational-Wave Observatory (LIGO). The Heisenberg limitisdescribed,alongwithNOONstatesandtheirapplicationinsuper-sensitivity, super-resolution,andquantumlithography.Applicationsofentanglementandcoin- cidence measurements are described including ghost imaging, quantum illumina- tion, absolute photodetector calibration, and interaction-free measurement. Light- matter interaction,atomicclocks,andatomcoolingandtrappingareincluded.The bookdoesnotcoverquantumcomputing,whichisatopictreatedbyanotherbookby theauthor[1].Togetherwithquantumcomputing,thetopicsofthisbookattemptto form an almost complete introductory description of the “second quantum revolution”. Sincethebookisintended fortheundergraduate beginner,Itrynottosay“itis easytoshow”toooften.Rigorousderivationsaregiven,althoughsomecalculations are completed as exercises in the book and heuristic arguments are occasionally employedtoavoidgettingboggeddowntoomuchincalculations.Theemphasisis onphysicalunderstanding.Thus,insomeinstances,asimplificationofthetopicsis presentedforpedagogicalreasons.Forexample,thecanonicalquantizationoflight v vi Preface is presented using entirely electric and magnetic fields, rather than the usual approach of using the vector potential. I do not use density matrices anywhere in this book. Students are expected to be familiar with the Dirac bra-ket notation and tensorproductofstates. Reference 1. RayLaPierre,IntroductiontoQuantumComputing(Springer,2021).https://doi. org/10.1007/978-3-030-69318-3 Acknowledgments Iam grateful toMcMaster University, theDepartment of EngineeringPhysics,my many colleagues, my students, and my family for inspiring me to write this book. Anyerrorsinthebookareentirelymyown. vii How to Use This Book Thisbookisintendedforasinglesemester(~12week)electivecourseonquantum optics,comprisedofapproximately361-hourlectures(3hoursperweek).Chapters are intended to be covered consecutively. Instructors may wish to begin with an overviewofthebra-ketnotation,innerproduct,expectationvalues,tensorproduct, andrelatedtopics.Asuggestedlecturescheduleis: Lecture1:Chap.1–CanonicalQuantization Lecture2–3:Chap.2–QuantumHarmonicOscillator Lecture4–5:Chap.3–CanonicalQuantizationofLight Lecture6:Chap.4–FockStatesandtheVacuum Lecture7:Chap.5–SinglePhotonState Lecture8–9:Chap.6–SinglePhotononaBeamSplitter Lecture10–11:Chap.7–SinglePhotoninanInterferometer Lecture12:Chap.8:Entanglement Lecture13–14:Chap.9–MultimodeQuantizedRadiation Lecture15–16:Chap.10–CoherentState Lecture17:Chap.11–CoherentStateonaBeamSplitter Lecture18–19:Chap.12–IncoherentState Lecture20–21:Chap.13–HomodyneandHeterodyneDetection Lecture22–23:Chap.14–CoherentStateinanInterferometer Lecture24–25:Chap.15–SqueezedLight Lecture26–27:Chap.16–SqueezedLightinanInterferometer Lecture28–29:Chap.17–HeisenbergLimit Lecture30–31:Chap.18–QuantumImaging Lecture32–33:Chap.19–Light–MatterInteraction Lecture34:Chap.20–AtomicClock Lecture35–36:Chap.21–AtomCoolingandTrapping The book assumes that students have successfully completed an introductory course in quantum mechanics, which is typically in the second year of a 4-year undergraduateprograminphysicsorrelateddisciplines.Thus,thisbookisintended ix x HowtoUseThisBook asacourseforthethirdorfourthyearofanundergraduateprogram,ortheentrylevel ofagraduateprogram. Each chapter includes exercises which can be completed by the student as homework assignments or used for tutorial instruction. A solutions manual is available from the publisher for qualified instructors. Each chapter also includes references for more advanced study, and further reading is listed at the end of thebook.