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1、LA-UR-93-1721SQUEEZEDSTATESFORGENERALSYSTEMSMichaelMartinNietoaaTheoreticalDivision,LosAlamosNationalLaboratoryUniversityofCaliforniaLosAlamos,NewMexico87545,U.S.A.D.RodneyTruaxbbDepartmentofChemistry,UniversityofCalgaryCalgary,AlbertaT2N1N4,CanadaABSTRACTWeproposealadder-opera
2、tormethodforobtainingthesqueezedstatesofgeneralsymmetrysystems.Itisageneralizationoftheannihilation-operatortechniqueforobtainingthecoherentstatesofsymmetrysystems.Weconnectthismethodwiththeminimum-uncertaintymethodforob-tainingthesqueezedandcoherentstatesofgeneralpotentialsyst
3、ems,andcommentonthedistinctionsbetweenthesetwomethodsandthedisplacement-operatormethod.PACS:03.65.-w,02.20.+b,42.50.-parXiv:hep-th/9308029v16Aug1993Coherentstatesareimportantinmanyfieldsoftheoreticalandexperimentalphysics[1,2].Similarly,thegeneralizationofcoherentstates,squeezed
4、states,hasbecomeofmoreandmoreinterestinrecenttimes[3,4].Thisisespeciallytrueinthefieldsofquantumoptics[5]andgravitationalwavedetection[6].However,onelimitationisthat,withtheexceptionwedescribebelow,essentiallyallworkonsqueezedstateshasconcentratedontheharmonicoscillatorsystem.In
5、thisletterwedescribeageneralizationofsqueezedstatestoarbitrarysymmetrysystems,anditsrelationshiptosqueezedstatesobtainedforgeneralpotentials.Webeginbyreviewingcoherentstatesandsqueezedstates.1)Displacement-OperatorMethod.Fortheharmonicoscillator,coherentstatesaredescribedbytheu
6、nitarydisplacementoperatoractingonthegroundstate[7,8]:Xn†∗12αD(α)
7、0i=exp[αa−αa]
8、0i=exp−
9、α
10、√
11、ni≡
12、αi.(1)2nn!ThegeneralizationofthismethodtoarbitraryLiegroupshasalonghistory[1,2,7,9].Onesimplyappliesthedisplacementoperator,whichistheunitaryexponentiationofthefactoralgebra,ontoan
13、extremalstate.Astosqueezedstates,thismethodhasbasicallyonlybeenappliedtoharmonicoscillator-likesystems[3,4].OneappliestheSU(1,1)displacementoperatorontothecoherentstate:∗D(α)S(z)
14、0i=
15、(α,z)i,S(z)=exp[zK+−zK−],(2)whereK+,K−,andK0formansu(1,1)algebraamongstthemselves:1††11†1K+=aa,
16、K−=aa,K0=(aa+),(3)2222[K0,K±]=±K±,[K+,K−]=−2K0.(4)Theo
