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-rw-r--r--dipole_elementRb87D1line.m177
-rw-r--r--rb87_D1_line.m25
2 files changed, 187 insertions, 15 deletions
diff --git a/dipole_elementRb87D1line.m b/dipole_elementRb87D1line.m
new file mode 100644
index 0000000..9235274
--- /dev/null
+++ b/dipole_elementRb87D1line.m
@@ -0,0 +1,177 @@
+function d=dipole_elementRb87D1line(Fl,ml,Fu,mu)
+% Fl, ml are F and m quantum numbers of lower state
+% Fu, mu are F and m quantum numbers of upper state
+% F is total momentum and m is projection
+ d.left = 0; %default return value
+ d.linear = 0; %default return value
+ d.right = 0; %default return value
+ if ( mu==(ml+1) )
+ % sigma plus polarization
+ % ------ Fl=2 -> Fu=2 --------
+ if ( (ml==-2) & (Fl==2) & (Fu==2) )
+ d.right=sqrt(1/6);
+ endif
+ if ( (ml==-1) & (Fl==2) & (Fu==2) )
+ d.right=sqrt(1/4);
+ endif
+ if ( (ml== 0) & (Fl==2) & (Fu==2) )
+ d.right=sqrt(1/4);
+ endif
+ if ( (ml== 1) & (Fl==2) & (Fu==2) )
+ d.right=sqrt(1/6);
+ endif
+ if ( (ml== 2) & (Fl==2) & (Fu==2) )
+ d.right=0;
+ endif
+ % ------ Fl=2 -> Fu=1 --------
+ if ( (ml==-2) & (Fl==2) & (Fu==1) )
+ d.right=sqrt(1/2);
+ endif
+ if ( (ml==-1) & (Fl==2) & (Fu==1) )
+ d.right=sqrt(1/4);
+ endif
+ if ( (ml== 0) & (Fl==2) & (Fu==1) )
+ d.right=sqrt(1/12);
+ endif
+ if ( (ml== 1) & (Fl==2) & (Fu==1) )
+ d.right=0;
+ endif
+ if ( (ml== 2) & (Fl==2) & (Fu==1) )
+ d.right=0;
+ endif
+ % ------ Fl=1 -> Fu=2 --------
+ if ( (ml==-1) & (Fl==1) & (Fu==2) )
+ d.right = -sqrt(1/12);
+ endif
+ if ( (ml== 0) & (Fl==1) & (Fu==2) )
+ d.right = -sqrt(1/4);
+ endif
+ if ( (ml== 1) & (Fl==1) & (Fu==2) )
+ d.right = -sqrt(1/2);
+ endif
+ % ------ Fl=1 -> Fu=1 --------
+ if ( (ml==-1) & (Fl==1) & (Fu==1) )
+ d.right = -sqrt(1/12);
+ endif
+ if ( (ml== 0) & (Fl==1) & (Fu==1) )
+ d.right = -sqrt(1/12);
+ endif
+ if ( (ml== 1) & (Fl==1) & (Fu==1) )
+ d.right = 0;
+ endif
+ endif
+ if ( mu==(ml+0) )
+ % pi polarization
+ % ------ Fl=2 -> Fu=2 --------
+ if ( (ml==-2) & (Fl==2) & (Fu==2) )
+ d.linear=-sqrt(1/3);
+ endif
+ if ( (ml==-1) & (Fl==2) & (Fu==2) )
+ d.linear=-sqrt(1/12);
+ endif
+ if ( (ml== 0) & (Fl==2) & (Fu==2) )
+ d.linear=0;
+ endif
+ if ( (ml== 1) & (Fl==2) & (Fu==2) )
+ d.linear=sqrt(1/12);
+ endif
+ if ( (ml== 2) & (Fl==2) & (Fu==2) )
+ d.linear=sqrt(1/3);
+ endif
+ % ------ Fl=2 -> Fu=1 --------
+ if ( (ml==-2) & (Fl==2) & (Fu==1) )
+ d.linear = 0;
+ endif
+ if ( (ml==-1) & (Fl==2) & (Fu==1) )
+ d.linear=sqrt(1/4);
+ endif
+ if ( (ml== 0) & (Fl==2) & (Fu==1) )
+ d.linear=sqrt(1/3);
+ endif
+ if ( (ml== 1) & (Fl==2) & (Fu==1) )
+ d.linear=sqrt(1/4);
+ endif
+ if ( (ml== 2) & (Fl==2) & (Fu==1) )
+ d.linear = 0;
+ endif
+ % ------ Fl=1 -> Fu=2 --------
+ if ( (ml==-1) & (Fl==1) & (Fu==2) )
+ d.linear = sqrt(1/4);
+ endif
+ if ( (ml== 0) & (Fl==1) & (Fu==2) )
+ d.linear = sqrt(1/2);
+ endif
+ if ( (ml== 1) & (Fl==1) & (Fu==2) )
+ d.linear = sqrt(1/4);
+ endif
+ % ------ Fl=1 -> Fu=1 --------
+ if ( (ml==-1) & (Fl==1) & (Fu==1) )
+ d.linear = sqrt(1/12);
+ endif
+ if ( (ml== 0) & (Fl==1) & (Fu==1) )
+ d.linear = 0;
+ endif
+ if ( (ml== 1) & (Fl==1) & (Fu==1) )
+ d.linear = -sqrt(1/12);
+ endif
+ endif
+ if ( mu==(ml-1) )
+ % sigma minus polarization
+ % ------ Fl=2 -> Fu=2 --------
+ if ( (ml==-2) & (Fl==2) & (Fu==2) )
+ d.left = 0;
+ endif
+ if ( (ml==-1) & (Fl==2) & (Fu==2) )
+ d.left = -sqrt(1/6);
+ endif
+ if ( (ml== 0) & (Fl==2) & (Fu==2) )
+ d.left = -sqrt(1/4);
+ endif
+ if ( (ml== 1) & (Fl==2) & (Fu==2) )
+ d.left = -sqrt(1/4);
+ endif
+ if ( (ml== 2) & (Fl==2) & (Fu==2) )
+ d.left = -sqrt(1/6);
+ endif
+ % ------ Fl=2 -> Fu=1 --------
+ if ( (ml==-2) & (Fl==2) & (Fu==1) )
+ d.left = 0;
+ endif
+ if ( (ml==-1) & (Fl==2) & (Fu==1) )
+ d.left = 0;
+ endif
+ if ( (ml== 0) & (Fl==2) & (Fu==1) )
+ d.left = sqrt(1/12);
+ endif
+ if ( (ml== 1) & (Fl==2) & (Fu==1) )
+ d.left = sqrt(1/4);
+ endif
+ if ( (ml== 2) & (Fl==2) & (Fu==1) )
+ d.left = sqrt(1/2);
+ endif
+ % ------ Fl=1 -> Fu=2 --------
+ if ( (ml==-1) & (Fl==1) & (Fu==2) )
+ d.left = -sqrt(1/2);
+ endif
+ if ( (ml== 0) & (Fl==1) & (Fu==2) )
+ d.left = -sqrt(1/4);
+ endif
+ if ( (ml== 1) & (Fl==1) & (Fu==2) )
+ d.left = -sqrt(1/12);
+ endif
+ % ------ Fl=1 -> Fu=1 --------
+ if ( (ml==-1) & (Fl==1) & (Fu==1) )
+ d.left = 0;
+ endif
+ if ( (ml== 0) & (Fl==1) & (Fu==1) )
+ d.left = sqrt(1/12);
+ endif
+ if ( (ml== 1) & (Fl==1) & (Fu==1) )
+ d.left = sqrt(1/12);
+ endif
+ endif
+endfunction
+
+
+
+% vim: ts=2:sw=2:fdm=indent
diff --git a/rb87_D1_line.m b/rb87_D1_line.m
index 1739df2..ea20e11 100644
--- a/rb87_D1_line.m
+++ b/rb87_D1_line.m
@@ -82,22 +82,15 @@ 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
+ if ( ( H0(j,j) < H0(k,k)) )
+ de=dipole_elementRb87D1line(...
+ total_momentum(j),m(j), ...
+ total_momentum(k),m(k) ...
+ );
+ dipole_elements.left(j,k) = de.left;
+ dipole_elements.right(j,k) = de.right;
+ dipole_elements.linear(j,k) = de.linear;
endif
endif
endfor
@@ -141,3 +134,5 @@ endfor
energy+=B_field * ( gm .* m);
% convert frequency to energy units
H0=diag(energy)*hbar;
+
+% vim: ts=2:sw=2:fdm=indent
generated by cgit v1.2.3 (git 2.39.1) at 2024-11-16 11:44:20 +0000