added code for lin EIT vs theta

2 files changed, 242 insertions, 0 deletions

diff --git a/compass_lin_extrema_vs_theta.m b/compass_lin_extrema_vs_theta.m
new file mode 100644
index 0000000..1c90f8c
--- /dev/null
+++ b/compass_lin_extrema_vs_theta.m
@@ -0,0 +1,155 @@
+1;
+clear all; 
+t0 = clock (); % we will use this latter to calculate elapsed time
+
+
+% load useful functions;
+useful_functions;
+
+% some physical constants
+useful_constants;
+
+basis_transformation; % load subroutines
+
+% load atom energy levels and decay description
+rb87_D1_line;
+%four_levels_with_polarization;
+%four_levels;
+%three_levels;
+%two_levels;
+
+% load EM field description
+field_description;
+
+%Nfreq=length(modulation_freq);
+
+
+
+%tune probe frequency
+detuning_p=0;
+N_detun_steps=100;
+%detuning_p_min=-B_field*gmg*4; % span  +/-4 Zeeman splitting
+%detuning_p_max=-detuning_p_min;
+detuning_freq=zeros(1,N_detun_steps+1);
+kappa_p      =zeros(1,N_detun_steps+1);
+kappa_m      =zeros(1,N_detun_steps+1);
+%detun_step=(detuning_p_max-detuning_p_min)/N_detun_steps;
+
+fprintf (stderr, "calculating atom properties\n");
+fflush (stderr);
+% calculate E_field independent properties of the atom
+% to be used as sub matrix templates for Liouville operator matrix
+[L0m, polarizability_m]=L0_and_polarization_submatrices( ...
+		Nlevels, ...
+		H0, g_decay, g_dephasing, dipole_elements ...
+		);
+elapsed_time = etime (clock (), t0);
+fprintf (stderr, "elapsed time so far is %.3f sec\n",elapsed_time);
+fflush (stderr);
+
+global atom_properties;
+atom_properties.L0m=L0m;
+atom_properties.polarizability_m=polarizability_m;
+atom_properties.dipole_elements=dipole_elements;
+
+%Ed=.1;     Edc=conj(Ed);
+%Ep=0.8*Ed;  Epc=conj(Ep);
+
+%light_positive_freq  = [wp, wd,  wp-wd];
+E_field_drive         = [0 , Ed,  0    ];
+E_field_probe         = [Ep, 0 ,  0    ];
+E_field_zero          = [0 , 0 ,  0    ];
+E_field_lab_pos_freq.linear = E_field_zero + (1.00000+0.00000i)*E_field_probe  + (1.00000+0.00000i)*E_field_drive; 
+%E_field_lab_pos_freq.right  = E_field_zero + (0.00000+0.00000i)*E_field_probe  + (0.00000+0.00000i)*E_field_drive;
+%E_field_lab_pos_freq.left   = E_field_zero + (0.00000+0.00000i)*E_field_probe  + (0.00000+0.00000i)*E_field_drive;
+
+
+% phi is angle between linear polarization and axis x
+phi=pi*2/4;
+% theta is angle between lab z axis (light propagation direction) and magnetic field axis (z')
+theta=pi/2;
+%theta=65/180*pi;
+
+%small ellipticity angle psi (0 to pi/2)
+% 0 will give linear polarization
+% pi/4 circular polarization
+%psi_el=pi/4;
+%psi_el=.2*pi/4;
+psi_el=0.0*pi/4;
+
+
+
+
+
+fprintf (stderr, "tuning laser in forloop to set conditions vs detuning\n");
+fflush (stderr);
+
+detuning_freq=[-.075, -.05, -.025, 0 , .025, .05 , .075, .1];
+
+problem_cntr=1;
+N_angle_steps=31;
+min_angle=0; max_angle=pi; 
+thetas=min_angle:((max_angle-min_angle)/N_angle_steps):max_angle;
+for theta=thetas;
+	for detuning_p_cntr=1:length(detuning_freq);
+
+			wp0=w_pf1;
+			wd=w_pf1-w_hpf_ground;
+			detuning_p=detuning_freq(detuning_p_cntr);
+			wp=wp0+detuning_p;
+			wm=wd-(wp-wd);
+
+		light_positive_freq=[ wp, wd, wp-wd];
+		% we define light as linearly polarized along x
+    E_field_lab_pos_freq.x = E_field_lab_pos_freq.linear;
+    E_field_lab_pos_freq.y = 0;
+    % now we add small elasticity
+    E_field_lab_pos_freq.y=sin(psi_el)*E_field_lab_pos_freq.x*(1i); % order is important
+    E_field_lab_pos_freq.x=cos(psi_el)*E_field_lab_pos_freq.x;
+		% set phi angle between light polarization and axis x
+		[E_field_lab_pos_freq.x, E_field_lab_pos_freq.y] = rotLinPolarization(phi, E_field_lab_pos_freq.x, E_field_lab_pos_freq.y);
+		E_field_lab_pos_freq.z=E_field_zero;
+
+
+		% now we transfor x,y,z, to x',y', and z' with respect to magnetic field az z' axis
+		E_field_pos_freq=xyz_lin2atomic_axis_polarization(theta, E_field_lab_pos_freq);
+
+		% we calculate dc and negative frequencies as well as amplitudes
+		[modulation_freq, E_field] = ...
+			light_positive_frequencies_and_amplitudes2full_set_of_modulation_frequencies_and_amlitudes(...
+				light_positive_freq, E_field_pos_freq);
+
+			freq_index=freq2index(wp,modulation_freq);
+
+			atom_field_problem.E_field          = E_field;
+			atom_field_problem.modulation_freq  = modulation_freq;
+			atom_field_problem.freq_index       = freq_index;
+
+			problems_cell_array{problem_cntr}=atom_field_problem;
+			problem_cntr++;
+
+
+			%kappa_p(detuning_p_cntr)=susceptibility_steady_state_at_freq( atom_field_problem);
+	endfor
+endfor
+
+save '/tmp/problem_definition.mat' problems_cell_array atom_properties  detuning_freq  theta;
+fprintf (stderr, "now really hard calculations begin\n");
+fflush (stderr);
+% once we define all problems the main job is done here
+%kappa_p=cellfun( @susceptibility_steady_state_at_freq, problems_cell_array);
+%kappa_p=parcellfun(2, @susceptibility_steady_state_at_freq, problems_cell_array);
+%[xi_linear, xi_left, xi_right]=parcellfun(2, @susceptibility_steady_state_at_freq, problems_cell_array);
+% strangely parcell is slower than cellfun 20 seconds vs 29
+%total_relative_transmission_vs_phi=parcellfun(2, @total_relative_transmission, problems_cell_array);
+total_relative_transmission=cellfun(@total_relative_transmission, problems_cell_array);
+
+%save 'xi_vs_detuning.mat' detuning_freq xi_linear xi_left xi_right  ;
+problem_cntr--;
+save '/tmp/total_relative_transmission_vs_theta.mat' detuning_freq total_relative_transmission thetas problem_cntr;
+
+compass_lin_extrema_vs_theta_output_results;
+
+elapsed_time = etime (clock (), t0)
+
+% vim: ts=2:sw=2:fdm=indent
diff --git a/compass_lin_extrema_vs_theta_output_results.m b/compass_lin_extrema_vs_theta_output_results.m
new file mode 100644
index 0000000..4e8d21b
--- /dev/null
+++ b/compass_lin_extrema_vs_theta_output_results.m
@@ -0,0 +1,87 @@
+1;
+
+
+load '/tmp/total_relative_transmission_vs_theta.mat' ;
+
+% let's create sideband transmission vs angle vectors
+% 1st of all we need to create matrix instead of a vector
+% with rows corresponding to absorption for each sideband
+% and columns to each phi angle
+
+N_detunings=length(detuning_freq);
+N_angles=length(thetas);
+
+transmission_matrix=reshape(total_relative_transmission, N_detunings, N_angles);
+
+% the last sideband is not in two-photon resonance
+% we use it as a reference for background transmission
+background_vector=transmission_matrix(N_detunings,:);
+background_transmission=repmat( background_vector , N_detunings, 1);
+
+transmission_matrix=-background_transmission+transmission_matrix;
+
+
+
+line_colors= [ ...
+	[ 0,   0,   1]; ...
+	[ 1,   0,   0]; ...
+	[ 0,   1,   0]; ...
+	[ 0,   0,   0]; ...
+	[ 0, 0.8,   0]; ...
+	[ 1,   0,   1]; ...
+	[ 0,   0,  .6] ...
+	];
+
+figure(1);
+clf();
+hold off;
+labels={};
+for i=1:N_detunings-1
+	%we will skip the very last row since it the reference transmission
+
+	zoom_factor=1;
+	%plot_style=strcat("-", num2str(i));
+	%plot( thetas, zoom_factor*(transmission_matrix(i,:)), plot_style);  
+	labels = {labels{:}, strcat("a_{", num2str(i-4), "}")};
+	line( thetas, zoom_factor*(transmission_matrix(i,:)), "color", line_colors(i,:) );  
+	hold on;
+endfor
+  
+set(gca, 'XTick', [0,pi/4, pi/2, 3*pi/4, pi])
+set(gca, 'XTickLabel', {'0', '\pi/4', '\pi/2', '3\pi/4', '\pi'})
+title("Relative sidebands amplitudes");
+xlabel('Angle \theta, between B-field and light propagation direction');
+ylabel("Amplitude");
+legend(labels);
+print('compass_circ_sidebands_vs_theta.png')
+
+hold off;
+
+figure(2)
+clf();
+j=4; k= 3;
+j=2; k= 7;
+% plotting parametric line of a sideband amplitude (j) vs another one (k)
+z = zeros(1,N_angles);
+col = thetas;  % This is the color, vary with x in this case.
+surface([zoom_factor*(transmission_matrix(j,:));zoom_factor*(transmission_matrix(j,:))], ...
+  [zoom_factor*(transmission_matrix(k,:));zoom_factor*(transmission_matrix(k,:))], ...
+  [z;z],[col;col],...
+  'facecol','no',...
+  'edgecol','interp',...
+  'linew',2);
+%plot(zoom_factor*(transmission_matrix(j,:)), zoom_factor*(transmission_matrix(k,:)))
+xlabel( labels{j});
+ylabel( labels{k});
+%clabel('\theta');
+colorbar;
+set(gca, 'ZTick', [0,pi/4, pi/2, 3*pi/4, pi])
+set(gca, 'ZTickLabel', {'0', '\pi/4', '\pi/2', '3\pi/4', '\pi'})
+
+%colorbar('Ticks',[0, pi/2, pi], 'TicksLabels', ['0', '\pi/2', '\pi'])
+%ctickslabel(['0', '\pi/2', '\pi'])
+title('One sideband amplitude vs another for different angles theta');
+print('compass_circ_sidebands_combo_vs_theta.png')
+
+
+% vim: ts=2:sw=2:fdm=indent