diff options
Diffstat (limited to 'xmds2')
| -rw-r--r-- | xmds2/Nlevels_no_dopler_no_z.example/Nlevels_no_dopler_no_z_from_mathematica.xmds | 68 |
1 files changed, 36 insertions, 32 deletions
diff --git a/xmds2/Nlevels_no_dopler_no_z.example/Nlevels_no_dopler_no_z_from_mathematica.xmds b/xmds2/Nlevels_no_dopler_no_z.example/Nlevels_no_dopler_no_z_from_mathematica.xmds index 04c7306..3f306c5 100644 --- a/xmds2/Nlevels_no_dopler_no_z.example/Nlevels_no_dopler_no_z_from_mathematica.xmds +++ b/xmds2/Nlevels_no_dopler_no_z.example/Nlevels_no_dopler_no_z_from_mathematica.xmds @@ -51,8 +51,8 @@ // repopulation rate (atoms flying in/out the laser beam) in MHz const double gt=0.01/2; // Natural linewidth of j's level in MHz - const double G3=2.7; - const double G4=3.0; + const double G3=2*2.7; + const double G4=2*3.0; // branching ratios const double R41=0.5, R42=0.5; @@ -68,7 +68,7 @@ complex E1c, E2c, Ecc; // Complex conjugated Rabi frequencies - //complex r21, r31, r41, r32, r42, r43; + complex r21, r31, r41, r32, r42, r43, r44; ]]> </globals> @@ -82,7 +82,9 @@ </geometry> <vector name="density_matrix" type="complex" dimensions="d1"> - <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 r21 r31 r41 r32 r42 r43</components>--> + <!--<components>r11 r22 r33 r44 r12 r13 r14 r23 r24 r34</components>--> + <components>r11 r22 r33 r12 r13 r14 r23 r24 r34</components> <!-- note one of the level population is redundant since r11+r22+r33+r44=1 @@ -92,14 +94,14 @@ <![CDATA[ // Note: // convergence is really slow if all populations concentrated at the bottom level |1> - // this is because if r11=1, everything else is 0 and then every small incriment + // 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 quicj and dirty fix I reshufle initial poulation + // 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 - r22 = 0.001; r33 = 0; r44 = 0; + r11 = 1; r22 = 0; r33 = 0; r12 = 0; r13 = 0; r14 = 0; r23 = 0; r24 = 0; r34 = 0; @@ -108,7 +110,7 @@ </vector> <sequence> - <integrate algorithm="ARK45" interval="600" tolerance="1e-3"> + <integrate algorithm="ARK89" interval="3" tolerance="1e-3"> <samples>128</samples> <operators> <integration_vectors>density_matrix</integration_vectors> @@ -117,30 +119,32 @@ E2c = conj(E2); Ecc = conj(Ec); - // r21=conj(r12); - // r31=conj(r13); - // r41=conj(r14); - // r32=conj(r23); - // r42=conj(r24); - // r43=conj(r34); - - // Equations of motions see page 1928 of the Frank's JMO paper - dr11_dt = gt - 2*gt*r11 + E1*i*(-r13 + r31) + 2*G3*r33*R31 + 2*G4*r44*R41; - dr12_dt = -2*gt*r12 + i*((-d1 + d2)*r12 - E2*r13 - Ec*r14 + E1*r32); - dr13_dt = -((G3 + 2*gt)*r13) + i*(-(E1*r11) - E2*r12 - d1*r13 + E1*r33); - dr14_dt = -((G4 + 2*gt)*r14) + i*(-(Ec*r12) - (d1 - d2 + d3)*r14 + E1*r34); - dr21_dt = -2*gt*r21 + i*((d1 - d2)*r21 - E1*r23 + E2*r31 + Ec*r41); - dr22_dt = gt - 2*gt*r22 + i*(-(E2*r23) - Ec*r24 + E2*r32 + Ec*r42) + 2*G3*r33*R32 + 2*G4*r44*R42; - dr23_dt = -((G3 + 2*gt)*r23) + i*(-(E1*r21) - E2*r22 - d2*r23 + E2*r33 + Ec*r43); - dr24_dt = -((G4 + 2*gt)*r24) + i*(-(Ec*r22) - d3*r24 + E2*r34 + Ec*r44); - dr31_dt = -((G3 + 2*gt)*r31) + i*(E1*r11 + E2*r21 + d1*r31 - E1*r33); - dr32_dt = -((G3 + 2*gt)*r32) + i*(E1*r12 + E2*r22 + d2*r32 - E2*r33 - Ec*r34); - dr33_dt = i*(E1*r13 + E2*r23 - E1*r31 - E2*r32) - 2*(G3 + gt)*r33; - dr34_dt = -((G3 + G4 + 2*gt)*r34) + i*(E1*r14 + E2*r24 - Ec*r32 + (d2 - d3)*r34); - dr41_dt = -((G4 + 2*gt)*r41) + i*(Ec*r21 + (d1 - d2 + d3)*r41 - E1*r43); - dr42_dt = -((G4 + 2*gt)*r42) + i*(Ec*r22 + d3*r42 - E2*r43 - Ec*r44); - dr43_dt = -((G3 + G4 + 2*gt)*r43) + i*(Ec*r23 - E1*r41 - E2*r42 + (-d2 + d3)*r43); - dr44_dt = Ec*i*(r24 - r42) - 2*(G4 + gt)*r44; + r21=conj(r12); + r31=conj(r13); + r41=conj(r14); + r32=conj(r23); + r42=conj(r24); + r43=conj(r34); + r44=1- r11 - r22 - r33; + + // Equations of motions according to Simon's mathematica code + dr11_dt = gt/2. - gt*r11 + E1*i*(-r13 + r31) + G3*r33*R31 + G4*r44*R41; + dr12_dt = -(gt*r12) + i*((-d1 + d2)*r12 - E2*r13 - Ec*r14 + E1*r32); + dr13_dt = -((G3 + 2*gt)*r13)/2. + i*(-(E1*r11) - E2*r12 - d1*r13 + E1*r33); + dr14_dt = -((G4 + 2*gt)*r14)/2. + i*(-(Ec*r12) - (d1 - d2 + d3)*r14 + E1*r34); + //dr21_dt = -(gt*r21) + i*((d1 - d2)*r21 - E1*r23 + E2*r31 + Ec*r41); + dr22_dt = gt/2. - gt*r22 + i*(-(E2*r23) - Ec*r24 + E2*r32 + Ec*r42) + G3*r33*R32 + G4*r44*R42; + dr23_dt = -((G3 + 2*gt)*r23)/2. + i*(-(E1*r21) - E2*r22 - d2*r23 + E2*r33 + Ec*r43); + dr24_dt = -((G4 + 2*gt)*r24)/2. + i*(-(Ec*r22) - d3*r24 + E2*r34 + Ec*r44); + //dr31_dt = -((G3 + 2*gt)*r31)/2. + i*(E1*r11 + E2*r21 + d1*r31 - E1*r33); + //dr32_dt = -((G3 + 2*gt)*r32)/2. + i*(E1*r12 + E2*r22 + d2*r32 - E2*r33 - Ec*r34); + dr33_dt = i*(E1*r13 + E2*r23 - E1*r31 - E2*r32) - (G3 + gt)*r33; + dr34_dt = -((G3 + G4 + 2*gt)*r34)/2. + i*(E1*r14 + E2*r24 - Ec*r32 + (d2 - d3)*r34); + //dr41_dt = -((G4 + 2*gt)*r41)/2. + i*(Ec*r21 + (d1 - d2 + d3)*r41 - E1*r43); + //dr42_dt = -((G4 + 2*gt)*r42)/2. + i*(Ec*r22 + d3*r42 - E2*r43 - Ec*r44); + //dr43_dt = -((G3 + G4 + 2*gt)*r43)/2. + i*(Ec*r23 - E1*r41 - E2*r42 + (-d2 + d3)*r43); + //dr44_dt = Ec*i*(r24 - r42) - (G4 + gt)*r44; + ]]> </operators> </integrate> |