1;
t0 = clock (); % we will use this latter to calculate elapsed time


% load useful functions;
useful_functions;

% some physical constants
useful_constants;

% load atom energy levels and decay description
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=-1;
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;
for detuning_p_cntr=1:N_detun_steps+1;

wp0=w12;
detuning_p=detuning_p_min+detun_step*(detuning_p_cntr-1);
wp=wp0+detuning_p;
wm=wd-(wp-wd);
%modulation_freq=[0,  wp, wd, wm,   -wp, -wd, -wm,  wp-wd, wd-wp];
%E_field        =[0,  Ep, Ed, Em,   Epc, Edc, Emc,  0,     0    ];
modulation_freq=[0,  wp, wd, -wp, -wd,  wp-wd, wd-wp];
E_field        =[0,  Ep, Ed,  Epc, Edc, 0,     0    ];
Nfreq=length(modulation_freq);

% now we create Liouville indexes list
[N, rhoLiouville_w, rhoLiouville_r, rhoLiouville_c]=unfold_density_matrix(Nlevels,Nfreq);
rhoLiouville=zeros(N,1);

% Liouville operator matrix construction
L=Liouville_operator_matrix( 
		N, 
		H0, g_decay, g_dephasing, dipole_elements,
		E_field, 
		modulation_freq, rhoLiouville_w, rhoLiouville_r, rhoLiouville_c
		);


%use the fact that sum(rho_ii)=1 to constrain solution
[rhoLiouville_dot, L]=constran_rho_and_match_L(
		N, L,
		modulation_freq, rhoLiouville_w, rhoLiouville_r, rhoLiouville_c);


%solving for density matrix vector
rhoLiouville=L\rhoLiouville_dot;


%rho_0=rhoOfFreq(rhoLiouville, 1, Nlevels, Nfreq); % 0 frequency, 
%rho_p=rhoOfFreq(rhoLiouville, 2, Nlevels, Nfreq); % probe frequency
%rho_d=rhoOfFreq(rhoLiouville, 3, Nlevels, Nfreq); % drive frequency
%rho_m=rhoOfFreq(rhoLiouville, 4, Nlevels, Nfreq); % opposite sideband frequency

kappa_p(detuning_p_cntr)=sucseptibility(2, rhoLiouville, dipole_elements, Nlevels, Nfreq);
%kappa_m(detuning_p_cntr)=sucseptibility(4, rhoLiouville, dipole_elements, Nlevels, Nfreq);
detuning_freq(detuning_p_cntr)=detuning_p;

%kappa_p_re=real(kappa_p);
%kappa_p_im=imag(kappa_p);

endfor
figure(1); plot(detuning_freq, real(kappa_p)); title("probe dispersion");
figure(2); plot(detuning_freq, imag(kappa_p)); title("probe absorption");
%figure(3); plot(detuning_freq, real(kappa_m)); title("off resonant sideband dispersion");
%figure(4); plot(detuning_freq, imag(kappa_m)); title("off resonant absorption");

elapsed_time = etime (clock (), t0)