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E-大學(xué)固體微結(jié)構(gòu)物理國(guó) Introduction:parity-time(PT)symmetryPTWaveguidebasedonsilicon:UnidirectionalmodetransformationUnidirectionalreflectionlesslightBlochoscillationin2Dparity-timePandTbrokenphotoniccrystalsNanjing量子力學(xué)基本公設(shè)之可觀測(cè)量公設(shè)(axiomof……量子系統(tǒng)的每次測(cè)量值必定 算子的本征值
xt HHH?HT'
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V*(x)V
n*(x)iiz2k 12k0n(x)Ai22m2VNanjingNanjingNanjingHHHPT ExceptionalExceptionalNat.Phys.6,192Nature488,167–171
Science33,729Nat.Mater.12,108
Nat.Phys.10,394Science346,328Nanjing量子力學(xué)的基本描述:厄密性問開放系統(tǒng)的量子力學(xué)的發(fā) 《近十年來10大物理發(fā)現(xiàn)NaturePhysics11,馬馬約拉納費(fèi)米磁單極PT對(duì)稱的光普朗克石墨拓?fù)浣^緣黑格斯玻色超光速中非測(cè)量的量子效測(cè)量的量子效NanjingNanjingParityandTimereversalsymmetryinQuantumNanjingCarlM.BenderCarlM.Bender,WashingtonK.G.Makris&R.El-Ganainy,UniversityofCentralHermiticity,PTsymmetryandreal ?
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V (pp,x (pp,iIfHisnotHermitian,thecommutationbetweenHandPTcanstillpreservewhensatisfyingfollowingcondition:?
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TheconditionsthatguaranteerealspectrumofShrodingerThecommutationbetweenHand
[??,?NanjingPTsymmetry:HandPTsharesimultaneouslythesameeigenNanjingPTsymmetrybroken—PTphase complexeigenPTSymmetricPhotonicCrystalsinIntegratedNanjingC.M.BenderandS.B?ttcher,PRL80,5243K.G.Makrisetal.,PRL100,103904A.Guoetal.,PRL103,093902C.E.Ruteretal.,NaturePhys.6,192T.Kottos,NaturePhys.6,166
a SymmetrybreakingtransversetolightpropagationPhys.Rev.Lett.103,093902Unidirectionalinvisibility:AsymmetryalonglightpropagationPhys.Rev.Lett.106,213901
NaturePhys.6,192NanjingNanjingEngineeringnanophotonicsinarealε- (gold,(gold,silver) ε(OE2003)Nature(2008)
photonicwaveguides(OEajing
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k11.9742 k20.9872NanjingNanjingThefirstorderL.Feng,etal,Science333,729EngineeringAsymmetricModeAsymmetricinter-bandtransitionwithafictionalDispersionofanSOIridge
Modeprofile,01Fundamental01FirstorderToachieveasymmetricconversion,weneedaspatialdielectricfunctionmodulation: NanjingParityandtimereversalsymmetry Inoursystem,theelectricfieldenvelopeSatisfiestheSchr?dinger-likeequation:
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???(x,z)?(x,z ???(x,z)?(x,zThenon-symmetricxandzdistribution:x,zparitysymmetryTheimaginarypartofmetalinz:ThePandTjoint:
time-reversalsymmetryBroken.PTsymmetryNanjingNanjingExceptionalpoint:PTsymmetrybreakingAttheexceptional emostremarkable:One-waylightamplificationisachievedfortheright
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Δz NanjingNanjingBrokentimereversalandparityExperiments:SiphotonicMaterialSiwaveguide:200nmx800nmGe/Crbilayer:11nmGe/18nmCrWorkingwavelength:1.55μmModulationwavelength:2.63μmNanjingIndexmodulationdesignforNanjing
IndexmodulationdesignforexperimentinSiwaveguideDeviceOverlayE-beamFabricationAlignmentmarks:e-beamlithographyandAuSisine-shapes:alignede-beamlithography,Sievaporationandlift-offGe/Crsineshapes:alignede-beamlithography,evapandlift-
NanjingSiwaveguide:alignede-beamlithography,ICP-RIEetchwithSF6/C4FNanjingDeviceCharacterization–NSOMSimulationresults–Poynting- -NSOMmeasured
- 6NanjingNanjingDeviceCharacterization–FourierUsingheterodyne L.Feng,etal,Science333,729A.Nesci,Y.Fainman,Proc.SPIE5181,62(2003)NanjingUnidirectionalinvisibilityUnidirectionalinvisibilityPTbroken T RLRRPTphase T1,RLPTsymmetric0 T RLRR2Unidirectional nzn(z)n0cos(2z)isin(2Z.Linetal.,Phys.Rev.Lett.106,231901L.Geetal.,Phys.Rev.A85,023802Phasetransitionatδ=classifiedbygeneralizedpower T UnidirectionalThePToptical Fourierspace:Introducingunidirectionalwavevectorof-UnidirectionalBragg
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Fengetal,NatureMaterials12,Modeprofile,|E|800
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SOIWaveguide:800nmX220nmSiwaveguideembeddedinWaveguideMode:FundamentalTEmode wavelength1550OpticalModulation:Bragggratingwith ypassivePT Implementationofnon-Hermitianopticsona EngineeringPTMaterialIn-phaseevolutionofPTopticalzzOpticalModulation:RealandimaginarypartsImaginaryPartModulation:Position
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sinq(z(z05 In-phase In-phasecomplexmodulationsmimicoriginalPT EngineeringPTMaterialDeviceimplementationusingrealisticequivalenteffective Im{Δε} EngineeringPT FinalSiwaveguide:220nmx800nmGe/Crbilayer:14nmGe/24nmCrPeriod:High-contrastunidirectional SuccessfullymimiclighttransportatPTphasetransition OverlayE-beamE-beamwritingalignmenterror:<Alignmentmarks:e-beamlithographyandAu bos:alignede-beamlithography,Sievaporationand bos:alignede-beamlithography,Ge/Crevap Siwaveguide:alignede-beam,hwithSF6/C4F8ExperimentalHowtomeasurereflectionsignalon-a-chipDevicetobemeasured+Directionalareintroducedforreflectionareintroducedtohavethepurefundamentalmodeinthedevice. Reflectionmeasuredthroughon-chipdirectional NanjingMeasuredopticalpropertiesofpassivePTBroadbandhigh-contrastasymmetricNanjing NatureMater.,February L.Feng,etal,Nature Blochoscillationin2DParity-TimesymmetricmaterialsBlochoscillationofelectronBlochmomentumofelectronbyDispersionrelationby
kcoskddkdkPositionofelectroninreal
zz
cosedEt NanjingPhys.Rev.Lett.83,4756Phys.Rev.Lett.83,4756Opt.Lett.23,1701Phys.Rev.Lett.83,963Indexgradientsrealizedwidthvarying,thermal-optic,electro-optics,bendingPhys.Rev.Lett.83,47522DPTsymmetricmetamaterials:Bloch2DPTsymmetricperiodicwaveguide:HermitandForphotonic StraightSiwaveguidearray:HermitianCoupling
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CroneverySiThickness:4nm
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QuantumHallEffect:OnewaypropagationinMOPCwithbrokenTimesymmetryQuantumSpinHallEffect:onewaypropagationwithTimereversionsymmetryNanjingNanjingHowabouttimereversalandparitysimultaneouslyMagneto-opticPhotonicCrystals:TimeTimereversalsymmetrybreakingbyappliedmagneticfield:MParitysymmetrybrokenYIG: 0 0
ChengHe,etal.,Phys.Rev.B83,075117NanjingNanjingPTsymmetricequifrequencysurface:y-cut Nanjing Onewaytransmission Nanjing P&Tsymmetric PP:kk,r???T:kk,r?r?,i?? 0
0 0
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