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-rw-r--r--xmds2/realistic_Rb/Makefile5
-rw-r--r--xmds2/realistic_Rb/tests/testsuite/realistic_Rb.xmds612
2 files changed, 5 insertions, 612 deletions
diff --git a/xmds2/realistic_Rb/Makefile b/xmds2/realistic_Rb/Makefile
index 34d73e1..ae7d4a9 100644
--- a/xmds2/realistic_Rb/Makefile
+++ b/xmds2/realistic_Rb/Makefile
@@ -47,8 +47,13 @@ $(png_targets): %.png : %.pdf
pdf: $(pdf_targets)
test:
+ cp $(XMDS_FILES) tests/testsuite/
cd tests; ./run_tests.py
+test_from_scratch:
+ rm -r tests/testsuite_results
+
+
$(pdf_targets): %.pdf : %.eps
cat $< | ps2eps -B > __tt.eps
epspdf __tt.eps $@
diff --git a/xmds2/realistic_Rb/tests/testsuite/realistic_Rb.xmds b/xmds2/realistic_Rb/tests/testsuite/realistic_Rb.xmds
deleted file mode 100644
index 5f7e437..0000000
--- a/xmds2/realistic_Rb/tests/testsuite/realistic_Rb.xmds
+++ /dev/null
@@ -1,612 +0,0 @@
-<?xml version="1.0"?>
-<simulation xmds-version="2">
- <testing>
- <arguments> --Ndens=1e15 --Lcell=10.0e-2 --Temperature=1e-3 --Pwidth=0.4e-6 --delta1=0 --delta2=0 --delta3=0 --E1o=0 --E2o=1e2 --E3o=0 --E4o=0</arguments>
- <xsil_file name="realistic_Rb.xsil" expected="realistic_Rb_expected.xsil" absolute_tolerance="1e-7" relative_tolerance="1e-5">
- <moment_group number="0" absolute_tolerance="1e-7" relative_tolerance="1e-6" />
- </xsil_file>
- </testing>
-
- <name>realistic_Rb</name>
-
- <author>Eugeniy Mikhailov</author>
- <description>
- License GPL.
-
- Solving simplified Rb atom model
- with fields propagation along spatial axis Z
- with 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.
-
-
- * --------------- | F=1, 2P_3/2 >
- * \ \
- * \ E3_r \ -------- | F=2, 2P_+1/2 >
- * \ E4_r \ / \
- * \ \ / E2_l \
- * \ / \ E1_l
- * | F=2, 2S_1/2 > -------------- \
- * \ \
- * \ \
- * ------------- | F=1, 2S_1/2 >
- *
-
-
- 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
- the upper level decay rate in the same units as Rabi frequency.
- </description>
-
- <features>
- <globals>
- <![CDATA[
- // Some numerical constants
- const double pi = M_PI;
-
- // atom related constants
- //read from Mathematica generated Constants.txt
- const double ha0 = 2.1471788680034824e10;
- const double ha1 = 2.558764384495815e9;
- const double g1 = 3.612847284945266e7;
- const double ha2 = 5.323020344462938e8;
- const double hb2 = 7.85178251911697e7;
- const double g2 = 3.8117309832741246e7;
- const double lambda1 = 0.00007949788511562656;
- const double lambda2 = 0.00007802412096860508;
- 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
- // 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
- const double mass = (86.909180527 * 1.660538921e-27); // atom mass in [kg]
- // above mass expression is written as (expression is isotopic_mass * atomic_mass_unit)
-
- // Average sqrt(v^2) in Maxwell distribution for one dimension
- // Maxwell related parameters will be calculated in <arguments> section
- double v_thermal_averaged=0;
- // Maxwell distribution velocities range to take in account in [m/s]
- double V_maxwell_min = 0, V_maxwell_max = 0;
-
- // repopulation rate (atoms flying in/out the laser beam) in [1/s]
- const double gt=0.01 *(2*M_PI*1e6);
-
- // Larmor frequency
- double WL=0;
-
-
-
- complex E1ac, E2ac, E3ac, E4ac; // Complex conjugated Rabi frequencies
-
-
- // inner use variables
- double probability_v; // will be used as p(v) in Maxwell distribution
-
- ]]>
- </globals>
- <validation kind="run-time"/> <!--allows to put ranges as variables-->
- <benchmark />
- <arguments>
- <!-- Rabi frequency divided by 2 in [1/s] -->
- <argument name="E1o" type="real" default_value="2*1.5*(2*M_PI*1e6)" />
- <argument name="E2o" type="real" default_value="0.05*(2*M_PI*1e6)" />
- <argument name="E3o" type="real" default_value="2*3.0*(2*M_PI*1e6)" />
- <argument name="E4o" type="real" default_value=".01*(2*M_PI*1e6)" />
- <!-- Fields detuning in [1/s] -->
- <argument name="delta1" type="real" default_value="0.0" />
- <argument name="delta2" type="real" default_value="0.0" />
- <argument name="delta3" type="real" default_value="0.0" />
- <!--Pulse duration/width [s] -->
- <argument name="Pwidth" type="real" default_value="0.1e-6" />
- <!-- Atom and cell properties -->
- <!--Cell length [m] -->
- <argument name="Lcell" type="real" default_value="1.5e-2" />
- <!--Density of atoms [1/m^3] -->
- <argument name="Ndens" type="real" default_value="1e15" />
- <!--Atoms temperature [K] -->
- <!--TODO: looks like Temperature > 10 K knocks solver,
- I am guessing detunings are too large and thus it became a stiff equation-->
- <!--! make sure it is not equal to zero!-->
- <argument name="Temperature" type="real" default_value="5" />
- <!-- This will be executed after arguments/parameters are parsed -->
- <!-- Read the code Luke: took me a while of reading the xmds2 sources to find it -->
- <![CDATA[
- // Average sqrt(v^2) in Maxwell distribution for one dimension
- if (Temperature == 0)
- _LOG(_ERROR_LOG_LEVEL, "ERROR: Temperature should be >0 to provide range for Maxwell velocity distribution\n");
- v_thermal_averaged=sqrt(k_boltzmann*Temperature/mass);
- // Maxwell distribution velocities range to take in account in [m/s]
- // there is almost zero probability for higher velocity p(4*v_av) = 3.3e-04 * p(0)
- V_maxwell_min = -4*v_thermal_averaged; V_maxwell_max = -V_maxwell_min;
-
- // 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 />
- <diagnostics />
- <fftw plan="estimate" threads="1" />
- <!--<fftw plan="patient" threads="1" />-->
- <!-- I don't see any speed up on 6 core CPU even if use threads="6" -->
- <!--<openmp />-->
- <auto_vectorise />
- <halt_non_finite />
- </features>
-
- <!-- 'z', 't', and 'v' to have dimensions [m], [s], and [m/s] -->
- <geometry>
- <propagation_dimension> z </propagation_dimension>
- <transverse_dimensions>
- <!-- IMPORTANT: looks like having a lot of points in time helps with convergence.
- I suspect that time spacing should be small enough to catch
- all pulse harmonics and more importantly 1/dt should be larger than
- the largest detuning (including Doppler shifts).
- Unfortunately calculation time is proportional to lattice size
- so we cannot just blindly increase it.
- Some rules of thumb:
- * lattice="1000" domain="(-1e-6, 1e-6)"
- was good enough detunings up to 155 MHz (980 rad/s) notice that 1/dt=500 MHz
- * lattice="10000" domain="(-1e-6, 1e-6)"
- works for Doppler averaging in up to 400K for Rb when lasers are zero detuned
- -->
- <dimension name="t" lattice="10000" domain="(-1e-6, 1e-6)" />
- <dimension name="v" lattice="2" domain="(V_maxwell_min, V_maxwell_max)" />
- </transverse_dimensions>
- </geometry>
-
- <!-- Rabi frequency -->
- <vector name="E_field" type="complex" initial_space="t">
- <components>E1 E2 E3 E4</components>
- <initialisation>
- <![CDATA[
- // Initial (at starting 'z' position) electromagnetic field does not depend on detuning
- // as well as time
- E1=E1o;
- E2=E2o*exp(-pow( ((t-0.0)/Pwidth),2) );
- E3=E3o;
- E4=E4o;
- ]]>
- </initialisation>
- </vector>
-
- <!--Maxwell distribution probability p(v)-->
- <computed_vector name="Maxwell_distribution_probabilities" dimensions="v" type="real">
- <components>probability_v</components>
- <evaluation>
- <![CDATA[
- // TODO: move to the global space/function. This reevaluated many times since it called from dependency requests but it never changes during the script lifetime since 'v' is fixed.
- probability_v=1.0/(v_thermal_averaged*sqrt(2*M_PI)) * exp( - mod2(v/v_thermal_averaged)/2.0 );
- ]]>
- </evaluation>
- </computed_vector>
-
- <!--Maxwell distribution norm sum(p(v))
- Needed since we sum over the grid instead of true integral,
- we also have finite cut off velocities-->
- <computed_vector name="Maxwell_distribution_probabilities_norm" dimensions="" type="real">
- <components>probability_v_norm</components>
- <evaluation>
- <dependencies basis="v">Maxwell_distribution_probabilities</dependencies>
- <![CDATA[
- // TODO: move to the global space/function. This reevaluated many times since it called from dependency requests but it never changes during the script lifetime since 'v' is fixed.
- probability_v_norm=probability_v;
- ]]>
- </evaluation>
- </computed_vector>
-
-
- <!-- Averaged across Maxwell distribution fields amplitudes -->
- <computed_vector name="E_field_avgd" dimensions="t" type="complex">
- <components>E1a E2a E3a E4a</components>
- <evaluation>
- <dependencies basis="v">E_field Maxwell_distribution_probabilities Maxwell_distribution_probabilities_norm</dependencies>
- <![CDATA[
- double prob_v_normalized=probability_v/probability_v_norm;
- E1a=E1*prob_v_normalized;
- E2a=E2*prob_v_normalized;
- E3a=E3*prob_v_normalized;
- E4a=E4*prob_v_normalized;
- ]]>
- </evaluation>
- </computed_vector>
-
- <!-- Averaged across Maxwell distribution density matrix components -->
- <computed_vector name="density_matrix_averaged" dimensions="t" type="complex">
- <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;
-
- 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>
- 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)-->
- <![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 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
-
- //read from Mathematica generated RbInits.txt
- 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;
- ]]>
- </initialisation>
- </vector>
-
- <sequence>
- <!--For this set of conditions ARK45 is faster than ARK89-->
- <!--ARK45 is good for small detuning when all frequency like term are close to zero-->
- <integrate algorithm="ARK45" tolerance="1e-5" interval="Lcell">
- <!--<integrate algorithm="SI" steps="200" interval="Lcell"> -->
- <!--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="100" 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-->
-
- <!--<integrate algorithm="SIC" interval="4e-2" steps="200">-->
-
- <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>
- <operator kind="cross_propagation" algorithm="SI" propagation_dimension="t">
- <integration_vectors>density_matrix</integration_vectors>
- <dependencies>E_field_avgd</dependencies>
- <boundary_condition kind="left">
- <!--This set boundary condition at all 'z' and left border of 't' (i.e. min(t))-->
- <!--
- <![CDATA[
- r11 = 0; r22 = 1; r33 = 0; r44 = 0;
- r12 = 0; r13 = 0; r14 = 0;
- r23 = 0; r24 = 0;
- r34 = 0;
- printf("z= %g, t= %g\n", z, t);
- ]]>
- -->
- </boundary_condition>
- <![CDATA[
- E1ac = conj(E1a);
- E2ac = conj(E2a);
- E3ac = conj(E3a);
- E4ac = conj(E4a);
-
- // Equations of motions according to Simon's mathematica code
- //read from Mathematica generated RbEquations.txt
- dr0101_dt = gt/8. - gt*r0101 + (g1*r0909)/2. + (g2*r1313)/6. - i*((r0113*E4a)/(4.*rt6) - (conj(r0113)*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. - (conj(r0214)*E4ac)/8.);
- dr0214_dt = (-(gt*r0214) - (gt + g2)*r0214)/2. - i*((WL*r0214)/2. - (-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3)*r0214 - (conj(r0602)*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. - (conj(r0309)*E1ac)/(4.*rt6) - (conj(r0315)*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) - (conj(r0703)*E2ac)/(4.*rt6) - (conj(r0915)*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) - (conj(r0703)*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) - (conj(r0410)*E1ac)/(4.*rt2) - (conj(r0416)*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) - (conj(r0804)*E2ac)/(4.*rt6) - (conj(r1016)*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) - (conj(r0804)*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. - (conj(r0511)*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. + (conj(r0214)*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) + (conj(r0614)*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. + (conj(r0309)*E2ac)/(4.*rt6) + (conj(r0315)*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. + (conj(r0709)*E2ac)/(4.*rt6) + (conj(r0715)*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) + (conj(r0915)*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) + (conj(r0410)*E2ac)/(4.*rt6) + (conj(r0416)*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) + (conj(r0810)*E2ac)/(4.*rt6) + (conj(r0816)*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) + (conj(r1016)*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) + (conj(r0309)*E1ac)/(4.*rt6) - (conj(r0709)*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) - (conj(r0709)*E3ac)/8. + (conj(r0309)*E4ac)/8.);
- dr1010_dt = -((gt + g1)*r1010) - i*(-(r0410*E1a)/(4.*rt2) + (r0810*E2a)/(4.*rt6) + (conj(r0410)*E1ac)/(4.*rt2) - (conj(r0810)*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) - (conj(r0810)*E3ac)/(4.*rt2) + (conj(r0410)*E4ac)/(4.*rt6));
- dr1111_dt = -((gt + g1)*r1111) - i*(-(r0511*E1a)/4. + (conj(r0511)*E1ac)/4.);
- dr1313_dt = -((gt + g2)*r1313) - i*(-(r0113*E4a)/(4.*rt6) + (conj(r0113)*E4ac)/(4.*rt6));
- dr1414_dt = -((gt + g2)*r1414) - i*((r0614*E3a)/(8.*rt3) - (r0214*E4a)/8. - (conj(r0614)*E3ac)/(8.*rt3) + (conj(r0214)*E4ac)/8.);
- dr1515_dt = -((gt + g2)*r1515) - i*((r0715*E3a)/8. - (r0315*E4a)/8. - (conj(r0715)*E3ac)/8. + (conj(r0315)*E4ac)/8.);
- dr1616_dt = -((gt + g2)*r1616) - i*((r0816*E3a)/(4.*rt2) - (r0416*E4a)/(4.*rt6) - (conj(r0816)*E3ac)/(4.*rt2) + (conj(r0416)*E4ac)/(4.*rt6));
- ]]>
- </operator>
- <!--
- According to xmds2 docs operator kind="ip" should be faster
- but our codes runs about 5% to 10% slower with it.
- Maybe because we very close to the stiff condition so I use "ex" kind
- <operator kind="ip" constant="yes">
- -->
- <operator kind="ex" constant="yes" type="imaginary">
- <operator_names>Lt</operator_names>
- <![CDATA[
- Lt = -i/c*kt;
- ]]>
- </operator>
- <integration_vectors>E_field</integration_vectors>
- <dependencies>density_matrix</dependencies>
- <![CDATA[
- //read from Mathematica generated RbPropEquations.txt
- dE1_dz = 0.16666666666666666*i*(2.449489742783178*conj(r0309) + 4.242640687119286*conj(r0410) + 6.*conj(r0511))*eta1 - Lt[E1];
- dE2_dz = -0.4082482904638631*i*(conj(r0709) + conj(r0810))*eta1 - Lt[E2];
- dE3_dz = -0.3333333333333333*i*(1.7320508075688772*conj(r0614) + 3.*conj(r0715) + 4.242640687119286*conj(r0816))*eta2 - Lt[E3];
- dE4_dz = (i*(2.449489742783178*conj(r0113) + 3*conj(r0214) + 3*conj(r0315) + 2.449489742783178*conj(r0416))*eta2)/3. - Lt[E4];
- ]]>
- </operators>
- </integrate>
- </sequence>
-
-
-
- <!-- The output to generate -->
- <output format="binary" filename="realistic_Rb.xsil">
- <group>
- <sampling basis="t(1000) " initial_sample="yes">
- <dependencies>E_field_avgd</dependencies>
- <moments>I1_out I2_out I3_out I4_out</moments>
- <![CDATA[
- I1_out = mod2(E1a);
- I2_out = mod2(E2a);
- I3_out = mod2(E3a);
- I4_out = mod2(E4a);
- ]]>
- </sampling>
- </group>
-
- <!--
- <group>
- <sampling basis="t(100) v(10)" initial_sample="yes">
- <dependencies>density_matrix_averaged</dependencies>
- <moments>
- 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
- </moments>
- <![CDATA[
- // populations output
- r11_out = r11a.Re();
- r22_out = r22a.Re();
- r33_out = r33a.Re();
- r44_out = r44a.Re();
- // coherences output
- r12_re_out = r12a.Re();
- r12_im_out = r12a.Im();
- r13_re_out = r13a.Re();
- r13_im_out = r13a.Im();
- r14_re_out = r14a.Re();
- r14_im_out = r14a.Im();
- r23_re_out = r23a.Re();
- r23_im_out = r23a.Im();
- r24_re_out = r24a.Re();
- r24_im_out = r24a.Im();
- r34_re_out = r34a.Re();
- r34_im_out = r34a.Im();
- ]]>
- </sampling>
- </group>
- -->
-
- <!-- use the following two groups only for debuging
- otherwise they are quite useless and have to much information
- in 3D space (z,t,v) -->
- <!--
- <group>
- <sampling basis="t(100) v(10)" initial_sample="yes">
- <dependencies>E_field</dependencies>
- <moments>I1_out_v I2_out_v I3_out_v I4_out_v</moments>
- <![CDATA[
- // light field intensity distribution in velocity subgroups
- I1_out_v = mod2(E1);
- I2_out_v = mod2(E2);
- I3_out_v = mod2(E3);
- I4_out_v = mod2(E4);
- ]]>
- </sampling>
- </group>
-
- <group>
- <sampling basis="t(100) v(10)" initial_sample="yes">
- <dependencies>density_matrix</dependencies>
- <moments>
- r11_out_v r22_out_v r33_out_v r44_out_v
- r12_re_out_v r12_im_out_v r13_re_out_v r13_im_out_v r14_re_out_v r14_im_out_v
- r23_re_out_v r23_im_out_v r24_re_out_v r24_im_out_v
- r34_re_out_v r34_im_out_v
- </moments>
- <![CDATA[
- // density matrix distribution in velocity subgroups
- // populations output
- r11_out_v = r11.Re();
- r22_out_v = r22.Re();
- r33_out_v = r33.Re();
- r44_out_v = r44.Re();
- // coherences output
- r12_re_out_v = r12.Re();
- r12_im_out_v = r12.Im();
- r13_re_out_v = r13.Re();
- r13_im_out_v = r13.Im();
- r14_re_out_v = r14.Re();
- r14_im_out_v = r14.Im();
- r23_re_out_v = r23.Re();
- r23_im_out_v = r23.Im();
- r24_re_out_v = r24.Re();
- r24_im_out_v = r24.Im();
- r34_re_out_v = r34.Re();
- r34_im_out_v = r34.Im();
- ]]>
- </sampling>
- </group>
- -->
-
- </output>
-
-</simulation>
-
-<!--
-vim: ts=2 sw=2 foldmethod=indent:
--->
generated by cgit v1.2.3 (git 2.39.1) at 2024-11-16 09:45:05 +0000