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2013QFSWhatisthequantumprojectionnoiseAnswer:Thequantumprojectionnoiseisbecauseofthepopulationfluctuationsofthequantumabsorbers.Considerasuitabletwo-levelsystemwithnarrowtransitionandresonancefrequencyothatisinterrogatedbyanelectromagneticfieldwithfrequencyclosetotheresonancefrequency.Iftheinternalstateisingeneralasuperpositionofthetwo|c1|1c2|2.Whenameasureisperformeditisdefinedwhetherthetwo-levelsystemhasabsorbedaphotonornot.Italsomeansthatthemeasurementprocessprojectsthetwo-levelatomeitherinstate|1>orinto|2>wherethephotonhasbeenabsorbedornotTodeterminethevariance2ofthemeasurementofthecalculated

P2|22|.Thevarianceis ^ 2(P2)2P2P22p(1p Asfollowsfromthequantumprojectionnoise,describedby,theuncertaintyofthemeasurementtofindtheatominstate|2>iszeroonlywheneitherp2=1or0.SoforanensembleofNparticlesthevarianceofthenumberofatomsintheexciterstateisgivenas:N2Np2(1p2Andassumingthatthenumberofquantumabsorbersprojectedontothestate|2>inafrequencystandardcanbedetectedwithprobabilityunity,theuncertaintyintheestimatedvalueof0canbederivedas:With(0)t/2andp2=1/2,theformerequationisderived11Soitcanbefoundthatthequantumprojectionnoisedependsonthenumberofdetectedatoms.AndthefundamentallimitofthequantumprojectionnoiseeffectstheAllanderivationandbyvaryingtheatomicnumbertheprincipallimitsetbythequantumprojectionnoisecouldbereached.IthasbeenreachedusingiontrapseitherwithasingleHg+ionorwithBe+.Calculatethespontaneousdecayratebetweenthetwohyperfinelevelsofthegroundstateof133Csand87Rb.Thenuclearspinsof133CsisI=7/2andof87RbisI=3/2.Sothegroundstateof133Cs62S1/2denotedasF=3andF’=4andfor87Rbground52S1/2denotedasF=1andF’=2.ItcanbedrewasByusingthepopulartransitionprobabilityformulaforMagneticDipoleTransition: j(j1)3/4l(l1)2eh jFIW 2j(j 2mc(2F1)(2F'1) j(j1)(j403hc2j1

F'wecanfoundCs=6.1*10-12s-1andRb=1.2*10-12s-ExplaintheoriginofMajoranapullinginatomicJ>1/2的原子在外磁场中纯塞曼分裂，Comparingwith(3.96),whythereisaPIin

1 KQS1 KQS/1 NNatNaswecansee,thePImaycomefromtheK.AndKisadIdependsonI(v).AndI(v)=Imax*(1+cos(2*PI(v-v0)T))/2,sowecansee TK andK=PI,whichisthedI(vv)*T the(7.11)hasa

WriteaprograminMathematicorMatlabtoplotaRamseyinterferencepatternusingreasonableCs-clockparameters.P(2'T)sin2(13/4sin2)1sin22Ial1sin4Ial Whatismagicwavelength?Howtocalcu