proper dipole elements for Rb87D1 line

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