1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
|
1;
useful_constants;
% 87Rb D1 line
%
% m=-2 m=-1 m=0 m=1 m=2
% ---- ---- ---- ---- ---- |P,F=2>
%
% ---- ---- ---- |P,F=1>
% m=-1 m=0 m=1
%
%
%
%
%
% m=-2 m=-1 m=0 m=1 m=2
% ---- ---- ---- ---- ---- |S,F=2>
%
% ---- ---- ---- |S,F=1>
% m=-1 m=0 m=1
w_hpf_ground=6834;
w_hpf_exited=817;
w_sf2 = w_hpf_ground; % Distance from |S,F=1> to |S,F=2>
w_pf1 =1e9; % something big Distance from |S,F=1> to |P,F=1>
w_pf2 = w_pf1+w_hpf_exited; %Distance from |S,F=1> to |P,F=2>
gmg=.7; % gyro magnetic ration for ground level
gme=.7; % gyro magnetic ration for exited level
%bottom level |F=1>
levels( 1)=struct( "ang_momentum", 0, "total_momentum", 1, "m", -1, "energy", 0, "gm", -gmg);
levels( 2)=struct( "ang_momentum", 0, "total_momentum", 1, "m", 0, "energy", 0, "gm", -gmg);
levels( 3)=struct( "ang_momentum", 0, "total_momentum", 1, "m", 1, "energy", 0, "gm", -gmg);
%second bottom level |F=2>
levels( 4)=struct( "ang_momentum", 0, "total_momentum", 2, "m", -2, "energy", w_sf2, "gm", gmg);
levels( 5)=struct( "ang_momentum", 0, "total_momentum", 2, "m", -1, "energy", w_sf2, "gm", gmg);
levels( 6)=struct( "ang_momentum", 0, "total_momentum", 2, "m", 0, "energy", w_sf2, "gm", gmg);
levels( 7)=struct( "ang_momentum", 0, "total_momentum", 2, "m", 1, "energy", w_sf2, "gm", gmg);
levels( 8)=struct( "ang_momentum", 0, "total_momentum", 2, "m", 2, "energy", w_sf2, "gm", gmg);
% first exited level |F=1>
levels( 9)=struct( "ang_momentum", 1, "total_momentum", 1, "m", -1, "energy", w_pf1, "gm", -gme);
levels(10)=struct( "ang_momentum", 1, "total_momentum", 1, "m", 0, "energy", w_pf1, "gm", -gme);
levels(11)=struct( "ang_momentum", 1, "total_momentum", 1, "m", 1, "energy", w_pf1, "gm", -gme);
% second exited level |F=2>
levels(12)=struct( "ang_momentum", 1, "total_momentum", 2, "m", -2, "energy", w_pf2, "gm", gme);
levels(13)=struct( "ang_momentum", 1, "total_momentum", 2, "m", -1, "energy", w_pf2, "gm", gme);
levels(14)=struct( "ang_momentum", 1, "total_momentum", 2, "m", 0, "energy", w_pf2, "gm", gme);
levels(15)=struct( "ang_momentum", 1, "total_momentum", 2, "m", 1, "energy", w_pf2, "gm", gme);
levels(16)=struct( "ang_momentum", 1, "total_momentum", 2, "m", 2, "energy", w_pf2, "gm", gme);
Nlevels=size(levels)(2);
H0=zeros(Nlevels);
ang_momentum = [1:Nlevels];
total_momentum = [1:Nlevels];
m = [1:Nlevels];
gm = [1:Nlevels];
for i=1:Nlevels
H0(i,i) = levels(i).energy;
ang_momentum(i) = levels(i).ang_momentum;
total_momentum(i) = levels(i).total_momentum;
m(i) = levels(i).m;
gm(i) = levels(i).gm;
endfor
H0=H0*hbar;
dipole_elements.left = zeros(Nlevels);
dipole_elements.right = zeros(Nlevels);
dipole_elements.linear = zeros(Nlevels);
for j=1:Nlevels
for k=1:Nlevels
if ( abs(ang_momentum(j) - ang_momentum(k)) == 1)
%transition allowed for L =L' +/- 1
% incorrect Clebsch-Gordan coefficients but should show some ideas
% but they correct within a factor, but not sign
if ( ((m(j)- m(k))==1) && ( H0(j,j) > H0(k,k)) )
dipole_elements.left(j,k)=1;
endif
if ( ((m(j)- m(k))==-1) && ( H0(j,j) > H0(k,k)) )
dipole_elements.right(j,k)=1;
endif
if ( ((m(j)- m(k))==0) && ( H0(j,j) > H0(k,k)) )
dipole_elements.linear(j,k)=1;
endif
endif
endfor
endfor
dipole_elements.linear+=dipole_elements.linear';
dipole_elements.left+=dipole_elements.left';
dipole_elements.right+=dipole_elements.right';
maximum_dipole_elements=dipole_elements.linear + dipole_elements.left + dipole_elements.right;
%defasing matrix
g_deph=0;
g_dephasing=zeros(Nlevels);
% dephasing only for non zero dipole elements (am I right?)
g_dephasing=g_deph*(abs(maximum_dipole_elements) != 0);
% decay matrix g(i,j) correspnds to decay from i-->j
gamma=6;
g_decay=zeros(Nlevels);
for i=1:Nlevels
for j=1:Nlevels
if ( H0(i,i) > H0(j,j) )
% only upper levels decaying and decay is always positive
g_decay(i,j)=gamma * abs( maximum_dipole_elements(i,j) );
endif
endfor
endfor
% ground level mixing need to be artificial
gamma_hpf=.001;
for i=1:Nlevels
for j=1:Nlevels
if ( abs( H0(i,i) - H0(j,j)) == w_hpf_ground )
% ground hyperfine are mixed together
g_decay(i,j)=gamma_hpf;
endif
endfor
endfor
|
