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1、PHYSICALREVIEWAVOLUME54,NUMBER6DECEMBER1996OptimalfrequencymeasurementswithmaximallycorrelatedstatesJ.J.Bollinger,WayneM.Itano,andD.J.WinelandTimeandFrequencyDivision,NationalInstituteofStandardsandTechnology,Boulder,Colorado80303D.J.HeinzenPhysicsDepartment,Univer
2、sityofTexas,Austin,Texas78712~Received16August1996!WeshowhowmaximallycorrelatedstatesofNtwo-levelparticlescanbeusedinspectroscopytoyieldafrequencyuncertaintyequalto(NT)21,whereTisthetimeofasinglemeasurement.Fromthetime-energyuncertaintyrelationweshowthatthisisthebe
3、stprecisionpossible.Werephrasetheseresultsinthelanguageofparticleinterferometryandobtainastateanddetectionoperatorwhichcanbeusedtoachieveaphaseuncertaintyexactlyequaltothe1/NHeisenberglimit,whereNisthenumberofparticlesusedinthemea-surement.@S1050-2947~96!50712-2#PA
4、CSnumber~s!:42.50.Dv,06.30.Ft,03.65.Bz,39.30.1wQuantumlimitstonoiseinspectroscopy@1±4#andinter-lating®elds@16#.TheRamseytechniqueisformallyequiva-ferometry@5±13#havebeenasubjectoffundamental,andtolenttoMach-Zehnderinterferometry@4,6#.Therefore,afteranincreasingdegr
5、ee,practicalinterest.Thisisespeciallytrueobtainingourresultsforoptimalfrequencymeasurements,forspectroscopyontrappedatomsorionswherethenumberwerephrasethemintermsofinterferometry.ofparticlesNis®xedandkeptsmalltoreduceundesiredReferences@2#and@4#discussthebasicideao
6、fusingperturbations.Naively,theuncertaintyofaspectroscopicorcorrelatedorsqueezedspinstatestoimprovetheprecisioninterferometricmeasurementislimitedbycountingstatisticsinspectroscopyfortheRamseytechniqueofseparatedoscil-tobeinverselyproportionaltoN1/2.However,anumber
7、oflating®elds.Webrie¯yreviewtheideahereandstartbyproposalshaveshownthatbyintroducingquantumcorrela-consideringthecaseofNuncorrelatedparticleswheretionsbetweentheparticles,themeasurementuncertaintycaneachparticleisinitiallypreparedinitsgroundstateug&.Thebereducedsot
8、hatitscalesinverselywithNratherthaninitialstateofthecompositesystemforthiscaseisequiva-N1/2@2±13#.Noneoftheideasdiscussedsofar,however,lenttotheu
