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Woon Siong Gan Quantum Acoustical Imaging Quantum Acoustical Imaging Woon Siong Gan Quantum Acoustical Imaging WoonSiongGan AcousticalTechnologiesSingaporePteLtd. Singapore,Singapore ISBN 978-981-19-0982-5 ISBN 978-981-19-0983-2 (eBook) https://doi.org/10.1007/978-981-19-0983-2 ©SpringerNatureSingaporePteLtd.2022 Thisworkissubjecttocopyright.AllrightsarereservedbythePublisher,whetherthewholeorpartof thematerialisconcerned,specificallytherightsoftranslation,reprinting,reuseofillustrations,recitation, broadcasting,reproductiononmicrofilmsorinanyotherphysicalway,andtransmissionorinformation storageandretrieval,electronicadaptation,computersoftware,orbysimilarordissimilarmethodology nowknownorhereafterdeveloped. Theuseofgeneraldescriptivenames,registerednames,trademarks,servicemarks,etc.inthispublication doesnotimply,evenintheabsenceofaspecificstatement,thatsuchnamesareexemptfromtherelevant protectivelawsandregulationsandthereforefreeforgeneraluse. Thepublisher,theauthorsandtheeditorsaresafetoassumethattheadviceandinformationinthisbook arebelievedtobetrueandaccurateatthedateofpublication.Neitherthepublishernortheauthorsor theeditorsgiveawarranty,expressedorimplied,withrespecttothematerialcontainedhereinorforany errorsoromissionsthatmayhavebeenmade.Thepublisherremainsneutralwithregardtojurisdictional claimsinpublishedmapsandinstitutionalaffiliations. ThisSpringerimprintispublishedbytheregisteredcompanySpringerNatureSingaporePteLtd. The registered company address is: 152 Beach Road, #21-01/04 Gateway East, Singapore 189721, Singapore ToRaymondStephens MyPh.D.Supervisor Preface I coined and invented the name quantum acoustical imaging for the extension of acoustical imaging from the classical regime to the quantum arena. This can be consideredaspartofquantumtechnology.Thetheoriesandbackgroundprinciples ofthisnewfieldaregivenindepthinthebookwiththeexamplesofsomepresent formsofavailableacousticalimagingwhichcanbeconsideredasquantumacous- tical imaging. The advantages of this new field are given such as the capability to godowntonanometreimageresolution.Mypersonalinventionsofquantumacous- ticalimagingarethatofasystembasedonphononsentanglementandthequantum ultrasound diffraction tomography system. Phonons entanglement is an important aspectofquantum theory.Thismodifies theclassicalRayleigh imagingresolution limittothequantumimageresolutionlimitbyafactorN,whereNisthenumberof phononsinvolvedinentanglementgiveninthedenominatoroftheformulaofimage resolution. An unique aspect of this book is that it has gone in depth into the quantum theoryofacousticalimagingsuchasphononsentanglement,superpositionprinciple andapplicationoftransporttheory.Quantummicrophonesandquantumtransducers are introduced. Examples of existing quantum acoustical imaging systems given aresasers,nanoultrasoundsystem,atomicforceacousticmicroscopeandultrasonic forcemicroscope. Towardstheendofthebook,thereisachapteronthesubjectofquantumimage processingwhichincludesquantumimagemodelsandquantumFouriertransform. Singapore WoonSiongGan January2022 vii Contents 1 QuantumTheory ............................................... 1 1.1 MathematicalFormulation .................................. 1 1.2 PropertiesofQuantumTheory .............................. 3 1.2.1 UncertaintyPrinciple ............................... 3 1.2.2 Entanglement ..................................... 6 1.3 Applications .............................................. 7 References ..................................................... 8 2 Entanglement .................................................. 9 2.1 HistoryofQuantumEntanglement ........................... 9 2.2 MeaningofEntanglement .................................. 9 2.3 TheEPRParadox ......................................... 10 2.4 MathematicalFormulationofQuantumEntanglement .......... 11 2.5 ApplicationsofQuantumEntanglement ...................... 12 References ..................................................... 12 3 ApplicationofTransportTheorytoQuantumAcousticalImaging .. 13 3.1 Introduction .............................................. 13 3.2 TransportPhenomena ...................................... 14 3.3 TransportTheory .......................................... 15 3.4 Electrons,Phonons,Electron-PhononInteraction .............. 16 References ..................................................... 17 4 Quantum Technologies—Quantum Sensors and Quantum ImagingSystems ............................................... 19 4.1 IntroductiontoQuantumTechnologies ....................... 19 4.2 QuantumAcousticMicrophones ............................. 19 4.3 QuantumUltrasoundTransducer ............................ 21 4.4 QuantumMicroscopy ...................................... 22 References ..................................................... 24 ix x Contents 5 UltrasonicForceMicroscope .................................... 25 5.1 ThePrincipleofUltrasonicForceMicroscope ................. 25 5.2 TheMechanicalDiodeEffect ............................... 26 5.3 Experimental Implementation of the Ultrasonic Force Microscope ............................................... 28 5.4 StudiesoftheUltrasonicForceMicroscopeData ............... 28 5.5 TheUltrasonicForceImages ................................ 29 5.6 Application of Ultrasonic Force Microscope toNanofabrication ......................................... 29 References ..................................................... 30 6 Sasers ......................................................... 31 6.1 SASERasaFormofQuantumAcousticalImaging ............. 31 6.2 GenerationandAmplificationofTerahertzAcousticWaves ...... 31 6.3 Theory of Electron Inversion and Phonon Amplification ProducedintheActiveSLbyOpticalPumping ................ 34 References ..................................................... 37 7 Nanoultrasound ................................................ 39 7.1 GenerationofNanoacousticWaves—OpticalPiezoelectric Transducer(OPT) ......................................... 39 7.2 OpticalDetectionofNanoacousticWaves ..................... 42 7.3 QuantumAcousticalImaging/Nanoimaging ................... 43 References ..................................................... 48 8 AtomicForceAcousticsMicroscope .............................. 49 8.1 Introduction .............................................. 49 8.2 ScanningProbeTechniqueandNanoindentation ............... 50 8.3 VibrationModesofAFMCantilevers ........................ 51 8.4 Linear Contact-Resonance Spectroscopy Using Flexural Modes ................................................... 51 8.5 FlexuralVibrationofClamped-FreeBeams ................... 52 8.6 ContactForcesasLinearSpringsandDashpots ................ 53 8.7 ImagingandContrastInversion ............................. 54 References ..................................................... 57 9 QuantumAcousticalImagingBasedonPhononsEntanglement ..... 59 9.1 PhononsEntanglementforQuantumAcousticalImaging ........ 59 9.2 MethodofGenerationofEntangledPhonons .................. 60 References ..................................................... 61 10 SuperpositionPrinciple ......................................... 63 10.1 TheGeneralPrinciple ...................................... 63 10.2 TheHistoryofSuperpositionPrinciple ....................... 64 10.3 FourierAnalysisandSuperpositionPrinciple .................. 64 10.4 SuperpositionPrincipleandBoundaryValueProblems ......... 64 Contents xi 10.5 SomeExamplesoftheApplicationsoftheSuperposition Principle ................................................. 65 10.6 InterferenceandSuperpositionPrinciple ...................... 65 10.7 TheQuantumVersionoftheRayleighResolutionLimit ......... 69 References ..................................................... 69 11 PhononsEntanglement ......................................... 71 11.1 GenerationofCoherentPhononsFieldsUsingImpulsive StimulatedRamanScattering(ISRS) ......................... 71 11.2 ExperimentalResults ...................................... 72 References ..................................................... 75 12 QuantumUltrasoundDiffractionTomography .................... 77 12.1 ClassicalUltrasoundDiffractionTomography ................. 77 12.2 QuantumConceptofTomography ........................... 77 12.3 ExtensiontoQuantumUltrasoundDiffractionTomography ...... 78 12.3.1 MathematicalFormulationofQuantumDiffraction Tomography ...................................... 78 12.4 Conclusions .............................................. 81 References ..................................................... 81 13 QuantumImageProcessing ..................................... 83 13.1 Introduction .............................................. 83 13.2 QuantumImageModels .................................... 84 13.3 QuantumFourierTransform(QFT) .......................... 85 13.4 Conclusions .............................................. 85 References ..................................................... 85 About the Author Dr.WoonSiongGanobtainedhisPh.D.attheageof24.Heisoneofthefoundersof condensedmatterphysics.Heisthefirsttointroducetransporttheoryintocondensed matter physics. He invented and coined the term transport theory in 1966 during his Ph.D. works at the physics department of Imperial College London. Transport theory is today the key foundation of the theoretical design of new materials. The statusoftransporttheoryincondensedmatterphysicsisequivalenttothatofYang Millstheoryinparticlephysics.HisPh.D.thesis(1969)usedstatisticalmechanics approachtodescribephasetransitionandultrasoundpropagationinsemiconductors in the presence of high magnetic fields and low temperatures instead of the usual methodofelectron–phononinteractionofmany-bodytheory.Thus,hisPh.D.(1969) thesis Transport Theory in Magnetoacoustics also played a role in the founding ofcondensedmatterphysics.In2007,heintroducedgaugeinvarianceapproachto acousticsfields,amilestoneinthehistoryofgaugeinvarianceinphysics.Recently,he alsointroducedcurvilinearspacetimeforthetreatmentofnonlinearacoustics.Due to the curved paths of high intensity acoustic fields, curvilinear spacetime should be used. He has the book Acoustical Imaging, Techniques and Applications for EngineerspublishedbyJohnWiley&Sonsin2012.HissecondbookNewAcoustics, basedonMetamaterials,waspublishedbySpringerinFebruary2018.Histhirdbook GaugeInvarianceApproachtoAcousticFieldswaspublishedbySpringerin2019. His fourth book Signal Processing and Image Processing for Acoustical Imaging was published by Springer in 2020. His fifth book Time Reversal Acoustics was published by Springer in 2021. His sixth book Nonlinear Acoustical Imaging was published by Springer in 2021. His current research interest is on transport theory approach to the phase transition, quantum acoustic metamaterials and curvilinear spacetimeapproachtononlinearacoustics. xiii