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-rw-r--r--xmds2/realistic_Rb/realistic_Rb.xmds355
1 files changed, 243 insertions, 112 deletions
diff --git a/xmds2/realistic_Rb/realistic_Rb.xmds b/xmds2/realistic_Rb/realistic_Rb.xmds
index 6a40191..598715f 100644
--- a/xmds2/realistic_Rb/realistic_Rb.xmds
+++ b/xmds2/realistic_Rb/realistic_Rb.xmds
@@ -44,14 +44,26 @@
<features>
<globals>
<![CDATA[
+ // Some numerical constants
const double pi = M_PI;
+ // proportional to splitting ratios sqrt(6) , sqrt(3), sqrt(2)
+ const double rt6 = 2.449489742783178;
+ const double rt3 = 1.7320508075688772;
+ const double rt2 = 1.4142135623730951;
+
+
const double c=3.e8;
const double k_boltzmann= 1.3806505e-23; // Boltzmann knostant in [J/K]
const double lambda=794.7e-9; //wavelength in m
- const double Kvec = 2*M_PI/lambda; // k-vector
+ // Fields k-vector
+ const double Kvec = 2*M_PI/lambda;
+ // Simplified k-vectors
+ const double Kvec1 = Kvec, Kvec2=Kvec, Kvec3=Kvec;
+
const double Gamma_super=6*(2*M_PI*1e6); // characteristic decay rate of upper level used for eta calculations expressed in [1/s]
// eta will be calculated in the <arguments> section
double eta = 0; // eta constant in the wave equation for Rabi frequency. Units are [1/(m s)]
+ double eta1=0, eta2=0, eta3=0;
// --------- Atom and cell properties -------------------------
// range of Maxwell distribution atomic velocities
@@ -66,18 +78,44 @@
// repopulation rate (atoms flying in/out the laser beam) in [1/s]
const double gt=0.01 *(2*M_PI*1e6);
+
// Natural linewidth of j's level in [1/s]
- const double G3=3.0 *(2*M_PI*1e6);
- const double G4=3.0 *(2*M_PI*1e6);
+ const double g1 = 3.612847284945266e7;
+ const double g2 = 3.8117309832741246e7;
+
+ // levels energy
+ const double ha0 = 2.1471788680034824e10;
+ const double ha1 = 2.558764384495815e9;
+ const double ha2 = 5.323020344462938e8;
+ const double hb2 = 7.85178251911697e7;
+
+ // Larmor frequency
+ double WL=0;
- // total decay of i-th level branching ratios. Rij branching of i-th level to j-th
- const double R41=0.5, R42=0.5;
- const double R31=0.5, R32=0.5;
complex E1ac, E2ac, E3ac, E4ac; // Complex conjugated Rabi frequencies
- complex r21, r31, r41, r32, r42, r43, r44; // density matrix elements
+ // density matrix elements which calculated via Hermitian property r_ij=conj(r_ji)
+ complex
+ r1301,
+ r1402,
+ r0903,
+ r1503,
+ r1004,
+ r1604,
+ r1105,
+ r0206,
+ r1406,
+ r0307,
+ r0907,
+ r1507,
+ r0408,
+ r1008,
+ r1608,
+ r1509,
+ r1610;
+
// inner use variables
double probability_v; // will be used as p(v) in Maxwell distribution
@@ -121,6 +159,10 @@
// eta constant in the wave equation for Rabi frequency. Units are [1/(m s)]
eta = 3*lambda*lambda*Ndens*Gamma_super/8.0/M_PI;
+ // !FIXME over simplification: we should use relevant levels linewidths
+ eta1 = eta;
+ eta2 = eta;
+ eta3 = eta;
]]>
</arguments>
<bing />
@@ -211,38 +253,119 @@
<!-- Averaged across Maxwell distribution density matrix components -->
<computed_vector name="density_matrix_averaged" dimensions="t" type="complex">
- <components>r11a r22a r33a r12a r13a r14a r23a r24a r34a r44a</components>
+ <components>
+ r0101a
+ r0113a
+ r0202a
+ r0214a
+ r0303a
+ r0309a
+ r0315a
+ r0404a
+ r0410a
+ r0416a
+ r0505a
+ r0511a
+ r0602a
+ r0606a
+ r0614a
+ r0703a
+ r0707a
+ r0709a
+ r0715a
+ r0804a
+ r0808a
+ r0810a
+ r0816a
+ r0909a
+ r0915a
+ r1010a
+ r1016a
+ r1111a
+ r1313a
+ r1414a
+ r1515a
+ r1616a
+ </components>
<evaluation>
<dependencies basis="v">density_matrix Maxwell_distribution_probabilities Maxwell_distribution_probabilities_norm</dependencies>
<![CDATA[
double prob_v_normalized=probability_v/probability_v_norm;
- r11a=r11*prob_v_normalized;
- r22a=r22*prob_v_normalized;
- r33a=r33*prob_v_normalized;
- r12a=r12*prob_v_normalized;
- r13a=r13*prob_v_normalized;
- r14a=r14*prob_v_normalized;
- r23a=r23*prob_v_normalized;
- r24a=r24*prob_v_normalized;
- r34a=r34*prob_v_normalized;
- r44a=r44*prob_v_normalized;
+
+ r0101a = r0101*prob_v_normalized;
+ r0113a = r0113*prob_v_normalized;
+ r0202a = r0202*prob_v_normalized;
+ r0214a = r0214*prob_v_normalized;
+ r0303a = r0303*prob_v_normalized;
+ r0309a = r0309*prob_v_normalized;
+ r0315a = r0315*prob_v_normalized;
+ r0404a = r0404*prob_v_normalized;
+ r0410a = r0410*prob_v_normalized;
+ r0416a = r0416*prob_v_normalized;
+ r0505a = r0505*prob_v_normalized;
+ r0511a = r0511*prob_v_normalized;
+ r0602a = r0602*prob_v_normalized;
+ r0606a = r0606*prob_v_normalized;
+ r0614a = r0614*prob_v_normalized;
+ r0703a = r0703*prob_v_normalized;
+ r0707a = r0707*prob_v_normalized;
+ r0709a = r0709*prob_v_normalized;
+ r0715a = r0715*prob_v_normalized;
+ r0804a = r0804*prob_v_normalized;
+ r0808a = r0808*prob_v_normalized;
+ r0810a = r0810*prob_v_normalized;
+ r0816a = r0816*prob_v_normalized;
+ r0909a = r0909*prob_v_normalized;
+ r0915a = r0915*prob_v_normalized;
+ r1010a = r1010*prob_v_normalized;
+ r1016a = r1016*prob_v_normalized;
+ r1111a = r1111*prob_v_normalized;
+ r1313a = r1313*prob_v_normalized;
+ r1414a = r1414*prob_v_normalized;
+ r1515a = r1515*prob_v_normalized;
+ r1616a = r1616*prob_v_normalized;
]]>
</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>-->
- <components>r11 r22 r33 r12 r13 r14 r23 r24 r34 r44</components>
- <!--
- note one of the level population is redundant since
- r11+r22+r33+r44=1
- so r11 is missing
- -->
+ <components>
+ r0101
+ r0113
+ r0202
+ r0214
+ r0303
+ r0309
+ r0315
+ r0404
+ r0410
+ r0416
+ r0505
+ r0511
+ r0602
+ r0606
+ r0614
+ r0703
+ r0707
+ r0709
+ r0715
+ r0804
+ r0808
+ r0810
+ r0816
+ r0909
+ r0915
+ r1010
+ r1016
+ r1111
+ r1313
+ r1414
+ r1515
+ r1616
+ </components>
<initialisation>
<!--This sets boundary condition at all times and left border of z (i.e. z=0)-->
- <!-- Comment out no light field initial conditions
<![CDATA[
// Note:
// convergence is really slow if all populations concentrated at the bottom level |1>
@@ -253,67 +376,39 @@
// 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;
+ r0101 = 0.125;
+ r0113 = 0;
+ r0202 = 0.125;
+ r0214 = 0;
+ r0303 = 0.125;
+ r0309 = 0;
+ r0315 = 0;
+ r0404 = 0.125;
+ r0410 = 0;
+ r0416 = 0;
+ r0505 = 0.125;
+ r0511 = 0;
+ r0602 = 0;
+ r0606 = 0.125;
+ r0614 = 0;
+ r0703 = 0;
+ r0707 = 0.125;
+ r0709 = 0;
+ r0715 = 0;
+ r0804 = 0;
+ r0808 = 0.125;
+ r0810 = 0;
+ r0816 = 0;
+ r0909 = 0;
+ r0915 = 0;
+ r1010 = 0;
+ r1016 = 0;
+ r1111 = 0;
+ r1313 = 0;
+ r1414 = 0;
+ r1515 = 0;
+ r1616 = 0;
]]>
- -->
- <!-- Below initialization assumes strong E1 and E3 which were shining for long time before
- we even start to look at the problem -->
- <!-- Precalculated by Nate via Mathematica steady state solver -->
- <dependencies>E_field_avgd</dependencies>
- <![CDATA[
- E1ac = conj(E1a);
- E2ac = conj(E2a);
- E3ac = conj(E3a);
- E4ac = conj(E4a);
-
- // IMPORTANT: assumes no detunings
- r11 = (gt*(4*mod2(E1a) + (G3 + gt)*(G3 + 2*gt))*((G4 +
- 2*gt)*(4*mod2(E3a) + gt*(G4 + gt)) + 4*mod2(E3a)*G4*(R41 -
- R42)))/(2.*(-16*mod2(E1a)*mod2(E3a)*G3*G4*R32*R41 + (G3 +
- 2*gt)*(4*mod2(E1a) + gt*(G3 + gt))*((G4 + 2*gt)*(4*mod2(E3a) +
- gt*(G4 + gt)) - 4*mod2(E3a)*G4*R42) + 4*mod2(E1a)*G3*R31*(-((G4 +
- 2*gt)*(4*mod2(E3a) + gt*(G4 + gt))) + 4*mod2(E3a)*G4*R42)));
-
- r13 = -((E1ac*gt*(G3 + gt)*i*((G4 + 2*gt)*(4*mod2(E3a) + gt*(G4 + gt))
- + 4*mod2(E3a)*G4*(R41 -
- R42)))/(-16*mod2(E1a)*mod2(E3a)*G3*G4*R32*R41 + (G3 +
- 2*gt)*(4*mod2(E1a) + gt*(G3 + gt))*((G4 + 2*gt)*(4*mod2(E3a) +
- gt*(G4 + gt)) - 4*mod2(E3a)*G4*R42) + 4*mod2(E1a)*G3*R31*(-((G4 +
- 2*gt)*(4*mod2(E3a) + gt*(G4 + gt))) + 4*mod2(E3a)*G4*R42)));
-
- r22 = (gt*(4*mod2(E3a) + (G4 + gt)*(G4 + 2*gt))*((G3 +
- 2*gt)*(4*mod2(E1a) + gt*(G3 + gt)) + 4*mod2(E1a)*G3*(-R31 +
- R32)))/(2.*(-16*mod2(E1a)*mod2(E3a)*G3*G4*R32*R41 + (G3 +
- 2*gt)*(4*mod2(E1a) + gt*(G3 + gt))*((G4 + 2*gt)*(4*mod2(E3a) +
- gt*(G4 + gt)) - 4*mod2(E3a)*G4*R42) + 4*mod2(E1a)*G3*R31*(-((G4 +
- 2*gt)*(4*mod2(E3a) + gt*(G4 + gt))) + 4*mod2(E3a)*G4*R42)));
-
- r24 = -((E3ac*gt*(G4 + gt)*i*((G3 + 2*gt)*(4*mod2(E1a) + gt*(G3 + gt))
- + 4*mod2(E1a)*G3*(-R31 +
- R32)))/(-16*mod2(E1a)*mod2(E3a)*G3*G4*R32*R41 + (G3 +
- 2*gt)*(4*mod2(E1a) + gt*(G3 + gt))*((G4 + 2*gt)*(4*mod2(E3a) +
- gt*(G4 + gt)) - 4*mod2(E3a)*G4*R42) + 4*mod2(E1a)*G3*R31*(-((G4 +
- 2*gt)*(4*mod2(E3a) + gt*(G4 + gt))) + 4*mod2(E3a)*G4*R42)));
-
- r33 = (2*mod2(E1a)*gt*((G4 + 2*gt)*(4*mod2(E3a) + gt*(G4 + gt)) +
- 4*mod2(E3a)*G4*(R41 -
- R42)))/(-16*mod2(E1a)*mod2(E3a)*G3*G4*R32*R41 + (G3 +
- 2*gt)*(4*mod2(E1a) + gt*(G3 + gt))*((G4 + 2*gt)*(4*mod2(E3a) +
- gt*(G4 + gt)) - 4*mod2(E3a)*G4*R42) + 4*mod2(E1a)*G3*R31*(-((G4 +
- 2*gt)*(4*mod2(E3a) + gt*(G4 + gt))) + 4*mod2(E3a)*G4*R42));
-
- r44 = (2*mod2(E3a)*gt*((G3 + 2*gt)*(4*mod2(E1a) + gt*(G3 + gt)) +
- 4*mod2(E1a)*G3*(-R31 +
- R32)))/(-16*mod2(E1a)*mod2(E3a)*G3*G4*R32*R41 + (G3 +
- 2*gt)*(4*mod2(E1a) + gt*(G3 + gt))*((G4 + 2*gt)*(4*mod2(E3a) +
- gt*(G4 + gt)) - 4*mod2(E3a)*G4*R42) + 4*mod2(E1a)*G3*R31*(-((G4 +
- 2*gt)*(4*mod2(E3a) + gt*(G4 + gt))) + 4*mod2(E3a)*G4*R42));
-
- ]]>
</initialisation>
</vector>
@@ -330,7 +425,8 @@
<!--<integrate algorithm="SIC" interval="4e-2" steps="200">-->
- <samples>100 100</samples>
+ <samples>100</samples>
+ <!--<samples>100 100</samples>-->
<!--Use the next line for debuging to see velocity dependence. Uncomment/switch on output groups 3,4-->
<!--<samples>100 100 100 100</samples>-->
<operators>
@@ -355,26 +451,59 @@
E3ac = conj(E3a);
E4ac = conj(E4a);
- 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 Nate's mathematica code
- dr11_dt = gt/2 - gt*r11 + i*(-(E1a*r13) - E4a*r14 + E1ac*r31 + E4ac*r41) + G3*r33*R31 + G4*r44*R41;
- dr12_dt = -(gt*r12) + i*((-(delta1 + Kvec*v) + (delta2 + Kvec*v))*r12 - E2a*r13 - E3a*r14 + E1ac*r32 + E4ac*r42);
- dr13_dt = -((G3 + 2*gt)*r13)/2. + i*(-(E1ac*r11) - E2ac*r12 - (delta1 + Kvec*v)*r13 + E1ac*r33 + E4ac*r43);
- dr14_dt = -((G4 + 2*gt)*r14)/2. + i*(-(E4ac*r11) - E3ac*r12 - ((delta1 + Kvec*v) - (delta2 + Kvec*v) + (delta3 + Kvec*v))*r14 + E1ac*r34 + E4ac*r44);
- dr22_dt = gt/2 - gt*r22 + i*(-(E2a*r23) - E3a*r24 + E2ac*r32 + E3ac*r42) + G3*r33*R32 + G4*r44*R42;
- dr23_dt = -((G3 + 2*gt)*r23)/2. + i*(-(E1ac*r21) - E2ac*r22 - (delta2 + Kvec*v)*r23 + E2ac*r33 + E3ac*r43);
- dr24_dt = -((G4 + 2*gt)*r24)/2. + i*(-(E4ac*r21) - E3ac*r22 - (delta3 + Kvec*v)*r24 + E2ac*r34 + E3ac*r44);
- dr33_dt = i*(E1a*r13 + E2a*r23 - E1ac*r31 - E2ac*r32) - (G3 + gt)*r33;
-
- dr34_dt = -((G3 + G4 + 2*gt)*r34)/2. + i*(E1a*r14 + E2a*r24 - E4ac*r31 - E3ac*r32 + ((delta2 + Kvec*v) - (delta3 + Kvec*v))*r34);
- dr44_dt = i*(E4a*r14 + E3a*r24 - E4ac*r41 - E3ac*r42) - (G4 + gt)*r44;
+ // Density matrix is Hermitian so we use r_ij=conj(r_ji)
+
+ r1301 = conj(r0113);
+ r1402 = conj(r0214);
+ r0903 = conj(r0309);
+ r1503 = conj(r0315);
+ r1004 = conj(r0410);
+ r1604 = conj(r0416);
+ r1105 = conj(r0511);
+ r0206 = conj(r0602);
+ r1406 = conj(r0614);
+ r0307 = conj(r0703);
+ r0907 = conj(r0709);
+ r1507 = conj(r0715);
+ r0408 = conj(r0804);
+ r1008 = conj(r0810);
+ r1608 = conj(r0816);
+ r1509 = conj(r0915);
+ r1610 = conj(r1016);
+
+ // Equations of motions according to Simon's mathematica code
+ dr0101_dt = gt/8. - gt*r0101 + (g1*r0909)/2. + (g2*r1313)/6. - i*((r0113*E4a)/(4.*rt6) - (r1301*E4ac)/(4.*rt6));
+ dr0113_dt = (-(gt*r0113) - (gt + g2)*r0113)/2. - i*(WL*r0113 - ((2*WL)/3. - delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3)*r0113 + (r0101*E4ac)/(4.*rt6) - (r1313*E4ac)/(4.*rt6));
+ dr0202_dt = gt/8. - gt*r0202 + (g1*r0909)/4. + (g1*r1010)/4. + (g2*r1313)/12. + (g2*r1414)/4. - i*((r0214*E4a)/8. - (r1402*E4ac)/8.);
+ dr0214_dt = (-(gt*r0214) - (gt + g2)*r0214)/2. - i*((WL*r0214)/2. - (-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3)*r0214 - (r0206*E3ac)/(8.*rt3) + (r0202*E4ac)/8. - (r1414*E4ac)/8.);
+ dr0303_dt = gt/8. - gt*r0303 + (g1*r0909)/12. + (g1*r1010)/3. + (g1*r1111)/12. + (g2*r1313)/4. + (g2*r1515)/4. - i*((r0309*E1a)/(4.*rt6) + (r0315*E4a)/8. - (r0903*E1ac)/(4.*rt6) - (r1503*E4ac)/8.);
+ dr0309_dt = (-(gt*r0309) - (gt + g1)*r0309)/2. - i*(-((-WL/6. - delta1 - v*Kvec1)*r0309) + (r0303*E1ac)/(4.*rt6) - (r0909*E1ac)/(4.*rt6) - (r0307*E2ac)/(4.*rt6) - (r1509*E4ac)/8.);
+ dr0315_dt = (-(gt*r0315) - (gt + g2)*r0315)/2. - i*(-(((-2*WL)/3. - delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3)*r0315) - (r0915*E1ac)/(4.*rt6) - (r0307*E3ac)/8. + (r0303*E4ac)/8. - (r1515*E4ac)/8.);
+ dr0404_dt = gt/8. - gt*r0404 + (g1*r1010)/4. + (g1*r1111)/4. + (g2*r1414)/4. + (g2*r1515)/12. + (g2*r1616)/6. - i*((r0410*E1a)/(4.*rt2) + (r0416*E4a)/(4.*rt6) - (r1004*E1ac)/(4.*rt2) - (r1604*E4ac)/(4.*rt6));
+ dr0410_dt = (-(gt*r0410) - (gt + g1)*r0410)/2. - i*(-(WL*r0410)/2. + (delta1 + v*Kvec1)*r0410 + (r0404*E1ac)/(4.*rt2) - (r1010*E1ac)/(4.*rt2) - (r0408*E2ac)/(4.*rt6) - (r1610*E4ac)/(4.*rt6));
+ dr0416_dt = (-(gt*r0416) - (gt + g2)*r0416)/2. - i*(-(WL*r0416)/2. - ((-4*WL)/3. - delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3)*r0416 - (r1016*E1ac)/(4.*rt2) - (r0408*E3ac)/(4.*rt2) + (r0404*E4ac)/(4.*rt6) - (r1616*E4ac)/(4.*rt6));
+ dr0505_dt = gt/8. - gt*r0505 + (g1*r1111)/2. + (g2*r1515)/6. + (g2*r1616)/3. - i*((r0511*E1a)/4. - (r1105*E1ac)/4.);
+ dr0511_dt = (-(gt*r0511) - (gt + g1)*r0511)/2. - i*(-(WL*r0511) - (WL/6. - delta1 - v*Kvec1)*r0511 + (r0505*E1ac)/4. - (r1111*E1ac)/4.);
+ dr0602_dt = -(gt*r0602) - i*(-(WL*r0602)/2. + (-WL/2. - delta1 + delta2 - v*Kvec1 + v*Kvec2)*r0602 + (r0614*E4a)/8. + (r1402*E3ac)/(8.*rt3));
+ dr0606_dt = gt/8. - gt*r0606 + (g1*r0909)/12. + (g1*r1010)/12. + (g2*r1313)/4. + (g2*r1414)/12. - i*(-(r0614*E3a)/(8.*rt3) + (r1406*E3ac)/(8.*rt3));
+ dr0614_dt = (-(gt*r0614) - (gt + g2)*r0614)/2. - i*((-WL/2. - delta1 + delta2 - v*Kvec1 + v*Kvec2)*r0614 - (-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3)*r0614 - (r0606*E3ac)/(8.*rt3) + (r1414*E3ac)/(8.*rt3) + (r0602*E4ac)/8.);
+ dr0703_dt = -(gt*r0703) - i*((-delta1 + delta2 - v*Kvec1 + v*Kvec2)*r0703 + (r0709*E1a)/(4.*rt6) + (r0715*E4a)/8. + (r0903*E2ac)/(4.*rt6) + (r1503*E3ac)/8.);
+ dr0707_dt = gt/8. - gt*r0707 + (g1*r0909)/12. + (g1*r1111)/12. + (g2*r1313)/4. + (g2*r1414)/3. + (g2*r1515)/4. - i*(-(r0709*E2a)/(4.*rt6) - (r0715*E3a)/8. + (r0907*E2ac)/(4.*rt6) + (r1507*E3ac)/8.);
+ dr0709_dt = (-(gt*r0709) - (gt + g1)*r0709)/2. - i*(-((-WL/6. - delta1 - v*Kvec1)*r0709) + (-delta1 + delta2 - v*Kvec1 + v*Kvec2)*r0709 + (r0703*E1ac)/(4.*rt6) - (r0707*E2ac)/(4.*rt6) + (r0909*E2ac)/(4.*rt6) + (r1509*E3ac)/8.);
+ dr0715_dt = (-(gt*r0715) - (gt + g2)*r0715)/2. - i*((-delta1 + delta2 - v*Kvec1 + v*Kvec2)*r0715 - ((-2*WL)/3. - delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3)*r0715 + (r0915*E2ac)/(4.*rt6) - (r0707*E3ac)/8. + (r1515*E3ac)/8. + (r0703*E4ac)/8.);
+ dr0804_dt = -(gt*r0804) - i*((WL*r0804)/2. + (WL/2. - delta1 + delta2 - v*Kvec1 + v*Kvec2)*r0804 + (r0810*E1a)/(4.*rt2) + (r0816*E4a)/(4.*rt6) + (r1004*E2ac)/(4.*rt6) + (r1604*E3ac)/(4.*rt2));
+ dr0808_dt = gt/8. - gt*r0808 + (g1*r1010)/12. + (g1*r1111)/12. + (g2*r1414)/12. + (g2*r1515)/4. + (g2*r1616)/2. - i*(-(r0810*E2a)/(4.*rt6) - (r0816*E3a)/(4.*rt2) + (r1008*E2ac)/(4.*rt6) + (r1608*E3ac)/(4.*rt2));
+ dr0810_dt = (-(gt*r0810) - (gt + g1)*r0810)/2. - i*((delta1 + v*Kvec1)*r0810 + (WL/2. - delta1 + delta2 - v*Kvec1 + v*Kvec2)*r0810 + (r0804*E1ac)/(4.*rt2) - (r0808*E2ac)/(4.*rt6) + (r1010*E2ac)/(4.*rt6) + (r1610*E3ac)/(4.*rt2));
+ dr0816_dt = (-(gt*r0816) - (gt + g2)*r0816)/2. - i*((WL/2. - delta1 + delta2 - v*Kvec1 + v*Kvec2)*r0816 - ((-4*WL)/3. - delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3)*r0816 + (r1016*E2ac)/(4.*rt6) - (r0808*E3ac)/(4.*rt2) + (r1616*E3ac)/(4.*rt2) + (r0804*E4ac)/(4.*rt6));
+ dr0909_dt = -((gt + g1)*r0909) - i*(-(r0309*E1a)/(4.*rt6) + (r0709*E2a)/(4.*rt6) + (r0903*E1ac)/(4.*rt6) - (r0907*E2ac)/(4.*rt6));
+ dr0915_dt = (-((gt + g1)*r0915) - (gt + g2)*r0915)/2. - i*((-WL/6. - delta1 - v*Kvec1)*r0915 - ((-2*WL)/3. - delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3)*r0915 - (r0315*E1a)/(4.*rt6) + (r0715*E2a)/(4.*rt6) - (r0907*E3ac)/8. + (r0903*E4ac)/8.);
+ dr1010_dt = -((gt + g1)*r1010) - i*(-(r0410*E1a)/(4.*rt2) + (r0810*E2a)/(4.*rt6) + (r1004*E1ac)/(4.*rt2) - (r1008*E2ac)/(4.*rt6));
+ dr1016_dt = (-((gt + g1)*r1016) - (gt + g2)*r1016)/2. - i*(-((delta1 + v*Kvec1)*r1016) - ((-4*WL)/3. - delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3)*r1016 - (r0416*E1a)/(4.*rt2) + (r0816*E2a)/(4.*rt6) - (r1008*E3ac)/(4.*rt2) + (r1004*E4ac)/(4.*rt6));
+ dr1111_dt = -((gt + g1)*r1111) - i*(-(r0511*E1a)/4. + (r1105*E1ac)/4.);
+ dr1313_dt = -((gt + g2)*r1313) - i*(-(r0113*E4a)/(4.*rt6) + (r1301*E4ac)/(4.*rt6));
+ dr1414_dt = -((gt + g2)*r1414) - i*((r0614*E3a)/(8.*rt3) - (r0214*E4a)/8. - (r1406*E3ac)/(8.*rt3) + (r1402*E4ac)/8.);
+ dr1515_dt = -((gt + g2)*r1515) - i*((r0715*E3a)/8. - (r0315*E4a)/8. - (r1507*E3ac)/8. + (r1503*E4ac)/8.);
+ dr1616_dt = -((gt + g2)*r1616) - i*((r0816*E3a)/(4.*rt2) - (r0416*E4a)/(4.*rt6) - (r1608*E3ac)/(4.*rt2) + (r1604*E4ac)/(4.*rt6));
]]>
</operator>
<!--
@@ -392,10 +521,10 @@
<integration_vectors>E_field</integration_vectors>
<dependencies>density_matrix</dependencies>
<![CDATA[
- dE1_dz = i*eta*conj(r13) +Lt[E1] ;
- dE2_dz = i*eta*conj(r23) +Lt[E2] ;
- dE3_dz = i*eta*conj(r24) +Lt[E3] ;
- dE4_dz = i*eta*conj(r14) +Lt[E4] ;
+ dE1_dz = 0.16666666666666666*eta1*(2.449489742783178*r0309 + 4.242640687119286*r0410 + 6.*r0511) - Lt[E1];
+ dE2_dz = -0.8164965809277261*eta1*(r0709 + r0810) - Lt[E2];
+ dE3_dz = -1.*eta2*(1.7320508075688772*r0614 + 3.*r0715 + 4.242640687119286*r0816) - Lt[E3];
+ dE4_dz = (4*eta2*(2.449489742783178*r0113 + 3*r0214 + 3*r0315 + 2.449489742783178*r0416))/3. - Lt[E4];
]]>
</operators>
</integrate>
@@ -418,6 +547,7 @@
</sampling>
</group>
+ <!--
<group>
<sampling basis="t(100) v(10)" initial_sample="yes">
<dependencies>density_matrix_averaged</dependencies>
@@ -449,6 +579,7 @@
]]>
</sampling>
</group>
+ -->
<!-- use the following two groups only for debuging
otherwise they are quite useless and have to much information
generated by cgit v1.2.3 (git 2.39.1) at 2024-11-16 09:27:20 +0000