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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'

H NanjingNanjing非PT對(duì)V*(x)V非PT對(duì)

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 ?

V ?

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V (pp,x (pp,iIfHisnotHermitian,thecommutationbetweenHandPTcanstillpreservewhensatisfyingfollowingcondition:?

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?(?)?(?)i??)????? ?(?)

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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

金屬材

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增益介電材NanjingUniversit16/53折射率調(diào)

PT對(duì)稱nR(x?)nR(?)?

折射率調(diào)NanjingUniversit17/53 SiliconcompatiblePTsymmetricphotonicSiliconwaveguide:301.4nmTwomodesat

k11.9742 k20.9872NanjingNanjingThefirstorderL.Feng,etal,Science333,729EngineeringAsymmetricModeAsymmetricinter-bandtransitionwithafictionalDispersionofanSOIridge

Modeprofile,01Fundamental01FirstorderToachieveasymmetricconversion,weneedaspatialdielectricfunctionmodulation: NanjingParityandtimereversalsymmetry Inoursystem,theelectricfieldenvelopeSatisfiestheSchr?dinger-likeequation:

E(x,z,t)(x,z)ei(kzti(x,z)H?(x,

k

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(2n?

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x ???(x,z)?(x,x ??(x,z)?(x,

???(x,z)?(x,z ???(x,z)?(x,zThenon-symmetricxandzdistribution:x,zparitysymmetryTheimaginarypartofmetalinz:ThePandTjoint:

time-reversalsymmetryBroken.PTsymmetryNanjingNanjingExceptionalpoint:PTsymmetrybreakingAttheexceptional emostremarkable:One-waylightamplificationisachievedfortheright

T 1 NanjingLeftNanjing.RightEngineeringAsymmetricModeequivalenteffectiveIm{Δε} Re{Δε}FundamentalFirstFundamentalFirstorderFirstorderFundamentalEffectiveEffectiveEffective0

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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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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

dAiA

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PTsymmetric2DphotonicSiwaveguidePeriod:500nmWidth:400nmThickness:

CroneverySiThickness:4nm

CurvedwaveguideCouplingradius:28.7μmNanjingNanjing2Dcurvedmetamaterials:HermitianandPTλ=500nm,w=400,Hermitian2Dphotonic PTsymmetric2Dλ=500nm,w=400,CouplingEqsofcurved

dAiA

A

n Effectivegradientandelectric

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BlochBzBBzB yNanjingBlochOscillationwithsecondaryNanjingThesupermodesofthearraycanbeΨm(n)ismodeoftheindividualwaveguide,Thewavenumberofthesupermodem,Wannier-StarkSecondaryemissiondueNanjingNanjing ParityandtimesymmetrybrokenphotonicPhotonicIntegerQuantumHallF.D.M.Haldaneetal.PRL.100,013904Z.Wangetal.PRL.100,Z.Wangetal.Nature461,Edgemodes:

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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NanjingNanjingP&Tsymmetricoperationsandrefraction Nanjing Handednessandrefractive NanjingNanjingEqua-frequencysurfaceforx-cutNanjingNanjingOne-wayphaseNanjing 3.Experiment:Symmetry-broken Y.Poo,C.He,etal.,Sci.R

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