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Equations for decay rates. Testing formulas for decay rates. N atoms inside a sphere: t heoretical prediction. Large wavelength. Wavelength 4 times larger than size of sphere. Wavelength equal to radius of sphere. Small wavelength. Dependence on shape. - PowerPoint PPT Presentation
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Testing formulas for decay ratesEquations for decay rates
)s(eigenvalue/ ,...,2,1)( F Ni
Ni
ji
rrk
rrkji
F
ji
jiij ,sin
,1
0
0
)(1:1 NN
)1(),1(:2 12)(
212)(
1 FFN NN
N atoms inside a sphere:theoretical prediction
1 where
,)()()(2
3
2/1
010102)(
in
rkjrkjrkjN
nnnNi
Large wavelength
Wavelength 4 times larger than size of sphere
Wavelength equal to radius of sphere
Small wavelength
Dependence on shape
Dependence on shape, large wavelength
Dependence on shape, wavelength larger than size
Dependence on shape, wavelength comparable with size
Dependence on shape, short wavelength
Superradiant state vector, large wavelength
Superradiant state vector,wavelength 4 times larger than size of sphere
Superradiant state vector, wavelength equal to radius of sphere
Superradiant state vector,small wavelength
Decay rates for different wavelength
0n
Decay rates for different wavelength
0n
3,2,1n
Decay rates for different wavelength
0n
3,2,1n
8,7,6,5,4n
15,...,10,9n
Calculating the decay rate of “superradiance” 0
Rk
Rk
Rk
NN
0
02
0
)(0 2
)2sin(1
)(2
3
max/,,...,3,2,1/,0, ,),()(nnmnNiiimninmn Yrkj
βΒβ
Tmax
Tmax )(,)( ΒΒSΒFΒF nn
.)()( polynomial of zerolargest :)( maxmaxmax0 nnn SF
. of instead )1( :matrix theof Size 2max Nn
Numerical results for 0
63.4
30.4)10(
......
28.3)2(
21.3)1(
48.2)0(
52.14/1/,1000
)(0
0
0
0
0
)(0
N
N
RN
55.46
39.46)4(
96.45)3(
19.44)2(
05.44)1(
90.39)0(
00.381/,1000
)(0
0
0
0
0
0
)(0
N
N
RN
