diff options
| -rw-r--r-- | xmds2/Nlevels_with_doppler_with_z_4wm/Nlevels_with_doppler_with_z_4wm.xmds | 40 |
1 files changed, 29 insertions, 11 deletions
diff --git a/xmds2/Nlevels_with_doppler_with_z_4wm/Nlevels_with_doppler_with_z_4wm.xmds b/xmds2/Nlevels_with_doppler_with_z_4wm/Nlevels_with_doppler_with_z_4wm.xmds index 8faa04d..ae2fe75 100644 --- a/xmds2/Nlevels_with_doppler_with_z_4wm/Nlevels_with_doppler_with_z_4wm.xmds +++ b/xmds2/Nlevels_with_doppler_with_z_4wm/Nlevels_with_doppler_with_z_4wm.xmds @@ -46,6 +46,7 @@ const double pi = M_PI; const double c=3.e8; const double lambda=794.7e-9; //wavelength in m + const double Kvec = 2*M_PI/lambda; // k-vector const double N=1e09*(1e6); //number of particles per cubic m i.e. density const double Gamma_super=6*(2*M_PI*1e6); // characteristic decay rate of upper level used for eta calculations expressed in [1/s] const double eta = 3*lambda*lambda*N*Gamma_super/8.0/M_PI; // eta constant in the wave equation for Rabi frequency. Units are [1/(m s)] @@ -64,6 +65,7 @@ complex E1c, E2c, E3c, E4c; // Complex conjugated Rabi frequencies complex r21, r31, r41, r32, r42, r43, r44; // density matrix elements + ]]> </globals> <benchmark /> @@ -89,7 +91,7 @@ <propagation_dimension> z </propagation_dimension> <transverse_dimensions> <dimension name="t" lattice="1000" domain="(-14.0e-7, 4.0e-7)" /> - <dimension name="v" lattice="1" domain="(-1000, 1000)" /> + <dimension name="v" lattice="10" domain="(-1000, 1000)" /> </transverse_dimensions> </geometry> @@ -108,6 +110,19 @@ </initialisation> </vector> + <!-- + <computed_vector name="E_field_avgd" dimensions="z t" type="complex"> + <components>E1a E2a E3a E4a</components> + <evaluation> + <dependencies basis="v">E_field</dependencies> + <![CDATA[ + // Calculate the current normalisation of the wave function. + ]]> + </evaluation> + </computed_vector> + --> + + <vector name="density_matrix" type="complex" initial_space="t"> <!--<components>r11 r22 r33 r44 r12 r13 r14 r23 r24 r34 r21 r31 r41 r32 r42 r43</components>--> <!--<components>r11 r22 r33 r44 r12 r13 r14 r23 r24 r34</components>--> @@ -196,7 +211,11 @@ <sequence> <!--For this set of conditions ARK45 is faster than ARK89--> - <integrate algorithm="ARK45" tolerance="1e-5" interval="1.5e-2"> + <!--ARK45 is good for small detuning when all frequency like term are close to zero--> + <!--<integrate algorithm="ARK45" tolerance="1e-5" interval="1.5e-2">--> + <!--RK4 is good for large detunings when frequency like term are big, it does not try to be too smart about adaptive step which ARK seems to make too small--> + <!--When ARK45 works it about 3 times faster then RK4 with 1000 steps--> + <integrate algorithm="RK4" steps="1000" tolerance="1e-5" interval="1.5e-2"> <!--SIC algorithm seems to be much slower and needs fine 'z' step tuning and much finer time grid--> <!--For example I had to quadruple the time grid from 1000 to 4000 when increased z distance from 0.02 to 0.04--> @@ -234,15 +253,15 @@ // Equations of motions according to Nate's mathematica code dr11_dt = gt/2 - gt*r11 + i*(-(E1*r13) - E4*r14 + E1c*r31 + E4c*r41) + G3*r33*R31 + G4*r44*R41; - dr12_dt = -(gt*r12) + i*((-delta1 + delta2)*r12 - E2*r13 - E3*r14 + E1c*r32 + E4c*r42); - dr13_dt = -((G3 + 2*gt)*r13)/2. + i*(-(E1c*r11) - E2c*r12 - delta1*r13 + E1c*r33 + E4c*r43); - dr14_dt = -((G4 + 2*gt)*r14)/2. + i*(-(E4c*r11) - E3c*r12 - (delta1 - delta2 + delta3)*r14 + E1c*r34 + E4c*r44); + dr12_dt = -(gt*r12) + i*((-(delta1 + Kvec*v) + (delta2 + Kvec*v))*r12 - E2*r13 - E3*r14 + E1c*r32 + E4c*r42); + dr13_dt = -((G3 + 2*gt)*r13)/2. + i*(-(E1c*r11) - E2c*r12 - (delta1 + Kvec*v)*r13 + E1c*r33 + E4c*r43); + dr14_dt = -((G4 + 2*gt)*r14)/2. + i*(-(E4c*r11) - E3c*r12 - ((delta1 + Kvec*v) - (delta2 + Kvec*v) + (delta3 + Kvec*v))*r14 + E1c*r34 + E4c*r44); dr22_dt = gt/2 - gt*r22 + i*(-(E2*r23) - E3*r24 + E2c*r32 + E3c*r42) + G3*r33*R32 + G4*r44*R42; - dr23_dt = -((G3 + 2*gt)*r23)/2. + i*(-(E1c*r21) - E2c*r22 - delta2*r23 + E2c*r33 + E3c*r43); - dr24_dt = -((G4 + 2*gt)*r24)/2. + i*(-(E4c*r21) - E3c*r22 - delta3*r24 + E2c*r34 + E3c*r44); + dr23_dt = -((G3 + 2*gt)*r23)/2. + i*(-(E1c*r21) - E2c*r22 - (delta2 + Kvec*v)*r23 + E2c*r33 + E3c*r43); + dr24_dt = -((G4 + 2*gt)*r24)/2. + i*(-(E4c*r21) - E3c*r22 - (delta3 + Kvec*v)*r24 + E2c*r34 + E3c*r44); dr33_dt = i*(E1*r13 + E2*r23 - E1c*r31 - E2c*r32) - (G3 + gt)*r33; - dr34_dt = -((G3 + G4 + 2*gt)*r34)/2. + i*(E1*r14 + E2*r24 - E4c*r31 - E3c*r32 + (delta2 - delta3)*r34); + dr34_dt = -((G3 + G4 + 2*gt)*r34)/2. + i*(E1*r14 + E2*r24 - E4c*r31 - E3c*r32 + ((delta2 + Kvec*v) - (delta3 + Kvec*v))*r34); dr44_dt = i*(E4*r14 + E3*r24 - E4c*r41 - E3c*r42) - (G4 + gt)*r44; ]]> </operator> @@ -266,11 +285,10 @@ - <!-- The output to generate --> <output format="binary" filename="Nlevels_with_doppler_with_z_4wm.xsil"> <group> - <sampling basis="t(1000)" initial_sample="yes"> + <sampling basis="t(100) v(10)" initial_sample="yes"> <dependencies>E_field</dependencies> <moments>I1_out I2_out I3_out I4_out</moments> <![CDATA[ @@ -283,7 +301,7 @@ </group> <group> - <sampling basis="t(100)" initial_sample="yes"> + <sampling basis="t(100) v(10)" initial_sample="yes"> <dependencies>density_matrix</dependencies> <moments> r11_out r22_out r33_out r44_out |