量子光学第二讲，相干态与压缩态 - 图文

压缩态压缩态的产生

压缩相干态α,ξ可以通过压缩真空然后平移，或者先平移真空然后在压缩相干态得到，即

α,ξ=S(ξ)D(α)0????????????????????α,ξ=D(α)S(ξ)0

????????(a)(b)????????????????????????????????????????????????(c)(d)2004 ?Dr. Shutian Liu, Department of Physics, Harbin Institute of Technology15

压缩态压缩态下场量的期望值和起伏

a=α,ξaα,ξ=0D+(α)S+(ξ)aS(ξ)D(α)0=α(acoshr?a+e2iφsinhr)α=αcoshr?α*e2iφsinhra2=a+2

*

=α,ξa2α,ξ

=0D+(a)S+(ξ)a2S(ξ)D(α)0=αS+(ξ)aS(ξ)S+(ξ)aS(ξ)α=αcoshr+(α

2

2

*24iφ

)e

sinh2r

?2α2e2iφsinhrcoshr?e2iφcoshrsinhr

aa=α

+

2

(coshr+sinhr)?(α)e

2

2

*22iφ

sinhrcoshr?α2e?2iφsinhrcoshr+sinh2r

16

2004 ?Dr. Shutian Liu, Department of Physics, Harbin Institute of Technology

压缩态旋转复振幅Y1+iY2=(X1+iX2)e?iφ=ae?iφ，因而它的分量的Y1和Y2的偏差为

(?Y1)2=Y12?Y1

2

=14(ae?iφ+a+eiφ)2?14(ae?iφ+a+eiφ)2

=1a2e?2iφ+a+2e2iφ+aa++a+

a?1(ae?iφ+a+eiφ44)2

=

1?24er(?Y1压缩因子r=ξ2)2=

4e2r压缩角φ?Y11??Y2=

4

(?N)2

=αcoshr?α*e2iφ

sinhr

2

+2cosh2rsinh2r

2004 ?Dr. Shutian Liu, Department of Physics, Harbin Institute of Technology

17

??????????????????????????????????相空间中压缩相干态的起伏

2004 ?Dr. Shutian Liu, Department of Physics, Harbin Institute of Technology

压缩态18

双光子相干态双光子相干态与压缩真空

压缩态产生是双光子过程，压缩态是标度变换相空间中的相干态。标度变换：在么正变换下将光子的产生和湮灭算符a和a+变换到另外一对相应的算符，令U为么正变换，则

b=UaU+b=μa+υa+

μ2?υ2=1

[b,b+]=1

变换之后的算符b(b+)所对应的波色子称为“准光子”，实际对应于双光子。算符b的本征态βg称为双光子相干态

bβ

g=ββg

与相干态的关系为

β

g

=Uα

2004 ?Dr. Shutian Liu, Department of Physics, Harbin Institute of Technology19