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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
B_field=.3;
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=.0; % gyro magnetic ration for exited level % CHECKME
%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);
energy = [1:Nlevels].*0;
ang_momentum = [1:Nlevels].*0;
total_momentum = [1:Nlevels].*0;
m = [1:Nlevels].*0;
gm = [1:Nlevels].*0;
for i=1:Nlevels
energy(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=diag(energy)*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;
if ( (m(j)==0) && ( total_momentum(j) == 1 ) && (total_momentum(k) == 1 ) )
% remember m=0 ->m'=0 is forbidden when F=1 and F'=1
% so we drop it back to zero
dipole_elements.linear(j,k)=0;
else
endif
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*hbar )
% ground hyperfine are mixed together
g_decay(i,j)=gamma_hpf;
endif
endfor
endfor
% apply B field Zeeman splitting
energy+=B_field * ( gm .* m);
% convert frequency to energy units
H0=diag(energy)*hbar;
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