From 55afa8456c8bb34999e5329cab385dd7354452c9 Mon Sep 17 00:00:00 2001 From: Eugeniy Mikhailov Date: Wed, 2 Nov 2011 23:45:56 -0400 Subject: Files renamed to reflect perturbative methods --- .../Nlevels_no_dopler_with_z.xmds | 315 --------------------- ...ls_no_dopler_with_z_4wm_with_perturbations.xmds | 315 +++++++++++++++++++++ .../Readme | 2 +- .../pp.m | 2 +- 4 files changed, 317 insertions(+), 317 deletions(-) delete mode 100644 xmds2/Nlevels_no_dopler_with_z_4wm_with_perturbations/Nlevels_no_dopler_with_z.xmds create mode 100644 xmds2/Nlevels_no_dopler_with_z_4wm_with_perturbations/Nlevels_no_dopler_with_z_4wm_with_perturbations.xmds (limited to 'xmds2') diff --git a/xmds2/Nlevels_no_dopler_with_z_4wm_with_perturbations/Nlevels_no_dopler_with_z.xmds b/xmds2/Nlevels_no_dopler_with_z_4wm_with_perturbations/Nlevels_no_dopler_with_z.xmds deleted file mode 100644 index 713231f..0000000 --- a/xmds2/Nlevels_no_dopler_with_z_4wm_with_perturbations/Nlevels_no_dopler_with_z.xmds +++ /dev/null @@ -1,315 +0,0 @@ - - - - Nlevels_no_dopler_with_z - - Eugeniy Mikhailov - - License GPL. - - Solving 4 level atom in N-field configuration, - with field propagation along spatial axis Z - no Doppler broadening - - We assume four-wave mixing condition when w3-w4=w2-w1 i.e. fields E3 and E4 drive the same - resonance as fields E2 and E1. - - - * --------------- |4> - * \ \ - * \ E3 \ -------- |3> - * \ E4 \ / \ - * \ \ / E2 \ - * \ / \ E1 - * |2> -------------- \ - * \ \ - * \ \ - * ------------- |1> - * - - We assume that E1 and and E3 are very strong and do not change during the propagations, - this leads to the assumption that r11,r22,r33,r44, r24, r13 are constant during all time. - - The hope is that it will give us significant speed up with just small drop in precision. - - - We are solving - dE/dz+(1/c)*dE/dt=i*eta*rho_ij, where j level is higher then i. - Note that E is actually a Rabi frequency of electromagnetic field not the EM field - in xmds terms it looks like - dE_dz = i*eta*rhoij - 1/c*L[E], here we moved t dependence to Fourier space - - VERY IMPORTANT: all Rabi frequency should be given in [1/s], if you want to - normalize it to something else look drho/dt equation. - No need to renormalizes eta as long as its express through i - the upper level decay rate in the same units as Rabi frequency. - - - - - - - - - - - - - - - - - - - - - - - - - - - z - - - - - - - - E1 E2 E3 E4 - - - - - - - - r11 r22 r33 r13 r24 r44 - - E_field - - - - - - r12 r14 r23 r34 - - - - // this is because if r11=1, everything else is 0 and then every small increment - // seems to be huge and adaptive solver makes smaller and smaller steps. - // As quick and dirty fix I reshuffle initial population - // so some of the population sits at the second ground level |2> - // TODO: Fix above. Make the equation of motion for r11 - // and express other level, let's say r44 - // through population normalization - // r11 = 1; r22 = 0; r33 = 0; r44 = 0; - // r12 = 0; r13 = 0; r14 = 0; - // r23 = 0; r24 = 0; - // r34 = 0; - ]]> - - - - - - - - - - - 200 200 - - - density_matrix - E_field zero_approximation_rho - - - - - - - Lt - - - E_field - density_matrix zero_approximation_rho - - - - - - - - - - - - - E_field - I1_out I2_out I3_out I4_out - - - - - - - density_matrix zero_approximation_rho - - r11_out r22_out r33_out r44_out - r12_re_out r12_im_out r13_re_out r13_im_out r14_re_out r14_im_out - r23_re_out r23_im_out r24_re_out r24_im_out - r34_re_out r34_im_out - - - - - - - - - diff --git a/xmds2/Nlevels_no_dopler_with_z_4wm_with_perturbations/Nlevels_no_dopler_with_z_4wm_with_perturbations.xmds b/xmds2/Nlevels_no_dopler_with_z_4wm_with_perturbations/Nlevels_no_dopler_with_z_4wm_with_perturbations.xmds new file mode 100644 index 0000000..8b89e9d --- /dev/null +++ b/xmds2/Nlevels_no_dopler_with_z_4wm_with_perturbations/Nlevels_no_dopler_with_z_4wm_with_perturbations.xmds @@ -0,0 +1,315 @@ + + + + Nlevels_no_dopler_with_z_4wm_with_perturbations + + Eugeniy Mikhailov + + License GPL. + + Solving 4 level atom in N-field configuration, + with field propagation along spatial axis Z + no Doppler broadening + + We assume four-wave mixing condition when w3-w4=w2-w1 i.e. fields E3 and E4 drive the same + resonance as fields E2 and E1. + + + * --------------- |4> + * \ \ + * \ E3 \ -------- |3> + * \ E4 \ / \ + * \ \ / E2 \ + * \ / \ E1 + * |2> -------------- \ + * \ \ + * \ \ + * ------------- |1> + * + + We assume that E1 and and E3 are very strong and do not change during the propagations, + this leads to the assumption that r11,r22,r33,r44, r24, r13 are constant during all time. + + The hope is that it will give us significant speed up with just small drop in precision. + + + We are solving + dE/dz+(1/c)*dE/dt=i*eta*rho_ij, where j level is higher then i. + Note that E is actually a Rabi frequency of electromagnetic field not the EM field + in xmds terms it looks like + dE_dz = i*eta*rhoij - 1/c*L[E], here we moved t dependence to Fourier space + + VERY IMPORTANT: all Rabi frequency should be given in [1/s], if you want to + normalize it to something else look drho/dt equation. + No need to renormalizes eta as long as its express through i + the upper level decay rate in the same units as Rabi frequency. + + + + + + + + + + + + + + + + + + + + + + + + + + + z + + + + + + + + E1 E2 E3 E4 + + + + + + + + r11 r22 r33 r13 r24 r44 + + E_field + + + + + + r12 r14 r23 r34 + + + + // this is because if r11=1, everything else is 0 and then every small increment + // seems to be huge and adaptive solver makes smaller and smaller steps. + // As quick and dirty fix I reshuffle initial population + // so some of the population sits at the second ground level |2> + // TODO: Fix above. Make the equation of motion for r11 + // and express other level, let's say r44 + // through population normalization + // r11 = 1; r22 = 0; r33 = 0; r44 = 0; + // r12 = 0; r13 = 0; r14 = 0; + // r23 = 0; r24 = 0; + // r34 = 0; + ]]> + + + + + + + + + + + 200 200 + + + density_matrix + E_field zero_approximation_rho + + + + + + + Lt + + + E_field + density_matrix zero_approximation_rho + + + + + + + + + + + + + E_field + I1_out I2_out I3_out I4_out + + + + + + + density_matrix zero_approximation_rho + + r11_out r22_out r33_out r44_out + r12_re_out r12_im_out r13_re_out r13_im_out r14_re_out r14_im_out + r23_re_out r23_im_out r24_re_out r24_im_out + r34_re_out r34_im_out + + + + + + + + + diff --git a/xmds2/Nlevels_no_dopler_with_z_4wm_with_perturbations/Readme b/xmds2/Nlevels_no_dopler_with_z_4wm_with_perturbations/Readme index f9eb2d3..04020fd 100644 --- a/xmds2/Nlevels_no_dopler_with_z_4wm_with_perturbations/Readme +++ b/xmds2/Nlevels_no_dopler_with_z_4wm_with_perturbations/Readme @@ -1,4 +1,4 @@ Fast light of field E2 -./Nlevels_no_dopler_with_z.run --delta1=0 --delta2=0 --delta3=0 --E1o=1.9e7 --E2o=3.1e5 --E3o=3.8e7 --E4o=6.3e4 +./Nlevels_no_dopler_with_z_4wm_with_perturbations.run --delta1=0 --delta2=0 --delta3=0 --E1o=1.9e7 --E2o=3.1e5 --E3o=3.8e7 --E4o=6.3e4 diff --git a/xmds2/Nlevels_no_dopler_with_z_4wm_with_perturbations/pp.m b/xmds2/Nlevels_no_dopler_with_z_4wm_with_perturbations/pp.m index 760aa82..9ca3195 100644 --- a/xmds2/Nlevels_no_dopler_with_z_4wm_with_perturbations/pp.m +++ b/xmds2/Nlevels_no_dopler_with_z_4wm_with_perturbations/pp.m @@ -1,4 +1,4 @@ -Nlevels_no_dopler_with_z +Nlevels_no_dopler_with_z_4wm_with_perturbations %% field propagation z_1=z_1*100; % z in cm -- cgit v1.2.3