diff options
| -rw-r--r-- | field_description.m | 11 | ||||
| -rw-r--r-- | liouville.m | 28 | ||||
| -rw-r--r-- | useful_constants.m | 1 | ||||
| -rw-r--r-- | useful_functions.m | 11 |
4 files changed, 38 insertions, 13 deletions
diff --git a/field_description.m b/field_description.m index ffe6bcc..5d8aa77 100644 --- a/field_description.m +++ b/field_description.m @@ -1,13 +1,16 @@ 1; %EM field definition -Ep=0.01; +Ep=0.01; %probe Epc=conj(Ep); -Ed=1; +Ed=.1; %drive Edc=conj(Ed); +Em=-Ep; % opposite sideband (resulting from EOM modulation of drive) +Emc=conj(Em); wd=w13; wp=w12; -modulation_freq=[0, wp, wd, -wp, -wd, wp-wd, wd-wp]; -E_field =[0, Ep, Ed, Epc, Edc, 0, 0 ]; +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, -wp]; %E_field =[0, Ep, Epc]; diff --git a/liouville.m b/liouville.m index 4812775..6fe83be 100644 --- a/liouville.m +++ b/liouville.m @@ -1,3 +1,6 @@ +1; +t0 = clock (); % we will use this latter to calculate elapsed time + % load useful functions; useful_functions; @@ -19,17 +22,19 @@ Nfreq=length(modulation_freq); %tune probe frequency detuning_p=0; N_detun_steps=100; -detuning_p_min=-15; +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; -modulation_freq=[0, wp, wd, -wp, -wd, wp-wd, wd-wp]; +wm=wd-(wp-wd); +modulation_freq=[0, wp, wd, wm, -wp, -wd, -wm, wp-wd, wd-wp]; % now we create Liouville indexes list [N, rhoLiouville_w, rhoLiouville_r, rhoLiouville_c]=unfold_density_matrix(Nlevels,Nfreq); @@ -49,22 +54,27 @@ L=Liouville_operator_matrix( 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); -rho_1=rhoOfFreq(rhoLiouville, 2, Nlevels, Nfreq); -rho_2=rhoOfFreq(rhoLiouville, 3, Nlevels, Nfreq); -%rho_l=rhoOfFreq(rhoLiouville, Nfreq, Nlevels, Nfreq) +%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)=sum(sum(rho_1)); +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)); -figure(2); plot(detuning_freq, imag(kappa_p)); +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) diff --git a/useful_constants.m b/useful_constants.m index 115efb4..82d1d1a 100644 --- a/useful_constants.m +++ b/useful_constants.m @@ -3,3 +3,4 @@ % some physical constants hbar=1; im_one=0+1i; +el_charge=1; diff --git a/useful_functions.m b/useful_functions.m index 5522afb..2ae4ced 100644 --- a/useful_functions.m +++ b/useful_functions.m @@ -141,3 +141,14 @@ function [rhoLiouville_dot, L]=constran_rho_and_match_L( rhoLiouville_dot(1)=1; endfunction +% calculate sucseptibility for the field at given frequency index +function kappa=sucseptibility(wi, rhoLiouville, dipole_elements, Nlevels, Nfreq) + + rho=rhoOfFreq(rhoLiouville, wi, Nlevels, Nfreq); + kappa=0; + for i=1:Nlevels + for j=1:Nlevels + kappa+=dipole_elements(j,i)*rho(i,j); + endfor + endfor +endfunction |