diff options
Diffstat (limited to 'psr/rb87_D1_line.m')
| -rw-r--r-- | psr/rb87_D1_line.m | 150 |
1 files changed, 150 insertions, 0 deletions
diff --git a/psr/rb87_D1_line.m b/psr/rb87_D1_line.m new file mode 100644 index 0000000..ecdd6a3 --- /dev/null +++ b/psr/rb87_D1_line.m @@ -0,0 +1,150 @@ +1; +useful_constants; + +% note all frequency values are in MHz + +% 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=.23; % gyro magnetic ration for exited level % CHECKME + +zeeman_splitting=0.0; +B_field=zeeman_splitting/gmg; + +%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); +% define dipole elements for transition from level j->k +for j=1:Nlevels + for k=1:Nlevels + if ( abs(ang_momentum(j) - ang_momentum(k)) == 1) + %transition allowed for L =L' +/- 1 + % but they correct within a factor, but not sign + 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 +endfor +dipole_elements.linear+=dipole_elements.linear'; +dipole_elements.left+=dipole_elements.left'; +dipole_elements.right+=dipole_elements.right'; + +maximum_dipole_elements=abs(dipole_elements.linear) + abs(dipole_elements.left) + abs(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=.0001; +for i=1:Nlevels + for j=1:Nlevels + % it would be better to introduce a level corresponding to the bath + % but this slows calculations + % So + % ground hyperfine are equally mixed together + if ( (abs( H0(i,i) - H0(j,j)) == w_hpf_ground*hbar ) || ... + (abs( H0(i,i) - H0(j,j)) == 0 ) ) + % i and j correspond to 2 ground levels + % we cannot decay to itself + if ( i != j ) + % total eight ground levels F=2 and F=1 so we decay in 7 channels + g_decay(i,j)+=gamma_hpf/7; + endif + endif + endfor +endfor + +% apply B field Zeeman splitting +energy+=B_field * ( gm .* m); +% convert frequency to energy units +H0=diag(energy)*hbar; + +% vim: ts=2:sw=2:fdm=indent |