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1、PHYSICALREVIEWD68,042001~2003!Squeezed-input,optical-spring,signal-recycledgravitational-wavedetectors121111JanHarms,YanbeiChen,SimonChelkowski,AlexanderFranzen,HenningVahlbruch,KarstenDanzmann,1andRomanSchnabel1InstitutfuÈrAtom-undMolekuÈlphysik,Uni
2、versitaÈtHannoverandMax-Planck-InstitutfuÈrGravitationsphysik(Albert-Einstein-Institut),Callinstr.38,30167Hannover,Germany2TheoreticalAstrophysics130-33,CaliforniaInstituteofTechnology,Pasadena,California91125,USA~Received26March2003;published21Augus
3、t2003!Wetheoreticallyanalyzethequantumnoiseofsignal-recycledlaserinterferometricgravitational-wavede-tectorswithadditionalinputandoutputoptics,namely,frequency-dependentsqueezingofthevacuumstateoflightenteringthedarkportandfrequency-dependenthomodyne
4、detection.WecombinetheworkofBuonannoandChenonthequantumnoiseofsignal-recycledinterferometerswithordinaryinputandoutputoptics,andtheworkofKimbleetal.onfrequency-dependentinputandoutputopticswithconventionalinterferometers.Analyticalformulasfortheoptim
5、alinputandoutputfrequencydependenciesareobtained.Itisshownthatinjectingsqueezedlightwiththeoptimalfrequency-dependentsqueezingangleintothedarkportyieldsanimprovementinthenoisespectraldensitybyafactorofe22r~inpower!overtheentiresqueezingbandwidth,wher
6、eristhesqueezingparameter.Itisfurthershownthatafrequency-dependent~variational!homodynereadoutleadstoanadditionalincreaseinsensitivitywhichissigni®cantinthewingsofthedoublyresonantstructure.Theoptimalvariationalinputsqueezinginthecaseofanordinaryoutp
7、uthomodynedetectionisshowntoberealizablebyapplyingtwooptical®ltersonafrequency-independentsqueezedvacuum.Through-outthispaper,wetakeasanexamplethesignal-recycledtopologycurrentlybeingcompletedattheGEO600site.However,theoreticalresultsobtainedherearea
8、lsoapplicabletotheproposedtopologyoftheAdvancedLIGO.DOI:10.1103/PhysRevD.68.042001PACSnumber~s!:04.80.Nn,03.65.Ta,42.50.Dv,95.55.YmI.INTRODUCTIONrecyclingisthereducedopticallossduetoimperfectmodematchingfromthemodehealingeffect@10#.Thenext-Gravitatio