48量子光学中的非经典态

191Vol.19,No.119993PROGRESSINPHYSICSMarch,1999(200030),;,::(1);(2),,:19980926;:199810250Planck-Einstein,1960,,[1]1997Nobel[2],,,,,:,Glauber,,,,Schrodinger,,,,,,(1),,E(r,t)=(h/20V)[aexp[i(kr-t)+h.c.](1)aa+,VL,V=L3h.c.k,()k,;00:00=c-2,c,(1),E(r,t)=E(r,t)(+)+E(r,t)(-)(2)E(r,t)(+)=h/20V)aexp[i(kr-t)],qpX1=(a+a+)/2,X2=(a-a+)/2i(3)r=0E(t)=Eo(X1cost+X2sint)Eo=2h/0V),X1X2[X1,X2]=i/2,,X1X21/4(4),X1(X2)1/2(5)(4),(2)N=a+aNN,FanoF=(N)2N(6)F=1,;F1,,;F1,(3),Hanbury-BrownTwiss(HBT)(1)M,,P1,P2;C,YoungMichelson,YoungMichelson,,g(1)(),g(1)()1HBT,-:I(r,t)I(r,t+),371:T,P1P2,r1r2rg(2)I(r,t)I(r,t+),g(2)(r,t,t+)=I(r,t)I(r,t+I(r,t)(I(r,t+)(7)I2(r,t)(I(r,t))2,g(2)(0)=I2(r,t)(I(r,t))21(8)Schwarz|I(r,t)I(r,t+)|2I2(r,t)I2(r,t+),g(2)()g(2)(0)(9),(8)(9)?,HBT,M,,,g(2)(0)=0,(8),,(8)(9),;,g(2)(),g(2)()=a+a+()a()aa+a2(10)=Tr(),,g(2)()tt+(9),c,,,cg(2)()g(2)(0)(11),g(2)(2)=1+F-1a+a(12)g(2)(0)1Fg(2)(0)1(13),(8),,,,1H=¶(a+a+1/2)(14)HN=a+a:N|n=n|n,|n,n,a|0=0¶/247191HBT|n,:|nn|=1,,,sasas+,|n1,n2,=|{ns}=|n1|n2(15)(1)X1=(2n+1)/2,X2=(2n+1)/2(16),F=0g(2)(n)(0)=1-1/n,,(2):n|E|n=0;E2,E:(E)2=n|E2|n=(¶/V)(n+1/2)(17)|0,,aa+,LambDirac22s1/222p1/2,LambRetherford[3],22s1/222p1/2100MHzLamb:,,,,,LambLambBetheWelton[4],:,,:sp,(3),,,(2):V-(2a)-(2b),VPac=ea|r|cPac=ea|r|cPbc=eb|r|cPab=ea|r|b:571:P(t)V=Pac(c3acc)exp(i1t)+Pbc(c3bcc)exp(i2t)+c.c(18)P(t)=Pac(c3acc)exp(i1t)+Pab(c3acb)exp(i2t)+c.c(19),V1=a-c,2=b-c;1=a-b,2=a-c2,E(+)=E1exp(-i1t)+E2exp(-i2t)|E(+)|2=|E1|2+|E2|2+{E31E2exp[i(1-2t)]}(),:|V(t)=6i=a,b,cci|i,0+c1|c,11+c2|,c,12|(t)=6i=a,b,cci|i,0+c1|b,11+c2|c,12|,=|á|v(t)|E(-)1E(+)2|v(t)=kexp[i(1-2)](20)(t)|E(-)1E(+)2|(t)=0(21):,:V12,,Young,()12,,(4),()=6nn(1+n)n+1|nn|(22)n=Tr(N)aa=a+a+=0,N2=2(n)2+nX1=X2=(2n+1)F=1+n,g(2)(0)=26719,Bose-Einstein,nn=n||n=nn(1+n)n+1(23)2?J(r,t)A(r,t)V(t)=d[J(r,t)A(r,t)]/c,Schrodinger|(t)=exp[(-i/¶)dtV(t)]|(0),|(t)=exp[Aa+-A3a]|(0)Aa+a,[5]|a=exp(a+-3a)|0(24a)|a=exp(-||2/2)exp(a+)|0(24b)=exp(-||2/2)6n=0(n/n!)|n(24c),|0|GlauberD()=exp(a+-3a)(25)(1)X1X2|X1=X2=1/2X1X2=1/4(26),,|E|E||2,E|E|,|a|2,,:D()|0||,|N|=||2(27a)|N2|=||4+||2(27b)FanoF=1,g(2)(0)=1,P(n)=nexp(-n)/n.(28)n=||2(27a)Bose-Einstein771:(2),q,o(q,0)=q|=exp(-||2/2)6(n/n!)q|n(29)q|n,n(q)=q|n=(/(2nn.))(-1)nexp(2/2)dndnexp(-2)=q,=(/¶)(1)(29),=(/2¶)1/2qo(),o(q,0)=(/¶)exp[(-/2¶)(q-qo)2](30),Glauber|,|,t=exp(-iHt/¶)|=exp(-it/2)|(t)(31)(t)=exp(-it)(30),o(q,t),,|o(q,t)|2=(/¶)1/2exp[-(q-qocost)2/¶](32),:t=0(q-qo),t=/2(m/2¶)exp[i(mqo|¶)q],t=(q+qo)(3),|=exp[-(||2-||2)/2+3](33)||d()=1(34)d()=d2/,d2=d(Re)d(Im)||,|=d()|exp(-||2/2)f(3)(35)f(3)=6(3/n.)n|(36)f(3)|0,0=6Cmna+man,|=0|f()=0(,5/5)f()(37)00(,5/5)8719a+,a5/5(38)Bargmann(4)[6]P(s)(,3)=-1d()exp(3-3)C(s)(,3)(39)C(s)(,3)=Tr(D())exp[s||2/2](40),Tr()=1s,s=1,P(s)(,3)=P(,3),P(41)s=-1,P(s)(,3)=Q(,3),Q(42)s=0,P(s)(,3)=W(,3),Wigner(43),,P(,3),Glauber:P(,3)=(2)(-o)(44):P(,3)=(1/n.)exp(||2)52553(2)()(45)()P,:P(,3)=n-1exp(-||2/n)(46)GaussQ(,3)W(,3):g(2)(0)=P(,3)||4d2[P(,3)||2d2]2=2g(2)(0)=1,,,,P;Q;WigncrX1=Re(),X2=Im(),(Re(),Im())|oWignerWc(,3)=2exp(-2|-o|2)(47)W=(),3(|o|2,),=||exp(i):|o,=,,971:3,g(2)(0)1(a+a+aa-a+a2)0,P,P(,3)(||2-a+a)2d()0,P(,3)0,(Xi)2(i=1,2)P(Xi)2=1/4+(Xi)2=1/4{1+d()P(,3)[(+3-(+3)]2},(Xi)21/4,P(,3),(5)(24):|,[7]b=a,-b,|b|0b,|0b=D()|0D()|0|0bD(),P=|0b0|=6m=0(-1)m(b+)mbmm.(48):bP=0;P2=P;P|nb=0,n0P|=6cnP|nb=co|0b,|co|2=|P|(49)|nbbFock|=|0b=exp(-||2/2)exp(a+)|0aco=exp(-||2/2)(6),(24)[8]|Z=exp(z3J--zJ+)|o(50)J+,J-Jo(su(2)),|oJ+=a+1a2,J-=a1a+2,Jo=(a1+a1-a+2a2)/2(50)(24)|12=[-(|1|2+|2|2)/2]cxp(1a+1+a+2)|00(51),,:0819|=exp(-||2/2)exp(-ia+1+3a+2+ia+1a+2)(52),(50)D(7)Schrodinger(S-Cat)[9],Schrodinger,,Schrodinger:,,S-CatS-Cat|S-Cat,1(|+|-)(53a)|S-Cat,2(||0)(53b),|S-Cat,1,(24c)n=,|S-Cat,1,|S-Cat,2S-Cat,S-Cat[10]S-Cat,S-Cat:;,,,,S-Cat,;((24)n=)S-Cat,,3,(4)(5),,,??,,,,?,H=P2/2m+kq2/2-eEo(Aq-Bq2)Aq,Bq2H=P2/2m+(k+2eBEo)q2/2-eAEoq,kkk=k+2eBEo,,(4)Bq2aaa+a+,181:4[11]|()=exp[(3aa-a+a+)/2]|0(54)=(1-||2)1/4exp[(-a+a+)/2]|0(55)=exp(i)tanh(||),=||exp(i)aa/2a+a+/2(a+1a1-a+2a2)/4su(1,1),(54)su(1,1)S()=cxp[(3aa-a+a+)/2](56),(1)|()(3)(=0,=),S()=exp[i(X1X2+X2X1)](57)(X1)|0=|01=(2/)1/4exp(-X21),|()()(X1)=X1|()=(2/)1/4exp(/2+2iX1X2)exp(-X21)=(2/2)1/4exp(-X21/2)(58a)=exp(-),X2=5/(2i5X1)(58a),(4)|()(X2),(X2)=X2|=(2/2)1/4exp(-X22/2)(58b),X1=5/(-2i5X2)|0=|02=(2/)1/4exp(-X22),=exp()(X1):X1,X12/4(X2):X2,X22/4,0(X1),(X2),(58),(X1)=S1|01S1=-1/2exp[-(-2-1)X21](59a)(X2)=S2|02S2=-1/2exp[-(-2-1)X22(59b)S1S2(59)Fouricr(59b)(X2)=[4(-2-1)]-1/2dX1exp[-X21/(4(-2-1))exp(-iX1X2|02,exp(-iX1X2|02=exp(X1/2(a+-a)|0)2,|X1/21(X2)=[41(1-2-1)]-1/2dX1exp[-X21/(4(1-2-1))|X1/22819=[(-2-1]-1/2dX1exp[-X2/(-2-1)|X(60)X=X12Jansky[10](2)|()S+aS=3a-a+(61a)SaS+=a+a+(61b)=cosh||,=eisinh||,||2-||2-1,/=eitanh||Y1+iY2=e(-i/2)(X1+iX2)(62)(X1+iX2)/2S+(Y1+iY2)S=Y1e(-||)+iY2e||(63)||0Y1,Y2|()Y1=e(-||)/2,Y2=e||/2(64)0,Y1(Y2)X1(X2)(3)N=()|N|()=||2N2=()|N2|()=2||2||2+||4F=2||2(65)g(2)(0)=3+1/||2(66)|()(4),|()[7]b=a+a+,b+=3a++3a(67)||2-||2=1Bogoliubov(61c,d)bS()=S()a,b+S()=S()a+(68)|()b|0b,|()|0S()|0b,,(54)S()Pb(67),,P|0=(1-1/2||2+3/8||4-5/16||6+){1-(1-||2+||4-||6+)(3a+2)/2+1/2.(1-||2+||4-||6+)(3