Shahriar_system xmds is ready

Still need to find good set of parameters to show fast light

Programmed code includes: xmds file, pp.m to show results and some
modifications of Simon's mathematica code to better suit xmds. Total
work time 1h30m including some EIT test cases.

1 files changed, 298 insertions, 0 deletions

diff --git a/xmds2/Shahriar_system/Nlevels_no_dopler_with_z.xsil b/xmds2/Shahriar_system/Nlevels_no_dopler_with_z.xsil
new file mode 100644
index 0000000..a3b05f2
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+++ b/xmds2/Shahriar_system/Nlevels_no_dopler_with_z.xsil
@@ -0,0 +1,298 @@
+<?xml version="1.0"?>
+<simulation xmds-version="2">
+
+        <name>Shahriar_system</name>
+
+        <author>Eugeniy Mikhailov, Simon Rochester</author>
+        <description>
+                License GPL.
+
+                Solving 3 level atom in double drive configuration
+                after Shahriar paper about white cavity
+                with field propagation along spatial axis Z
+                no Doppler broadening.
+
+                All fields detuned from upper level i.e. Raman configuration
+
+
+                *
+                *         .....
+                *           /   ....
+                *          / .... \
+                *         /   /    \
+                *        /   /-------- |3>  
+                *       E3  /        \
+                *      /   E2         \ 
+                *     /   /            \ E1
+                *    ------ |2>         \
+                *                        \
+                *                    ------- |1>
+                *
+
+
+                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.
+        </description>
+
+        <features>
+                <globals>
+                        <![CDATA[
+                                const double pi = M_PI; 
+                                const double c=3.e8;
+                                const double lambda=794.7e-9; //wavelength in m
+                                const double N=1e10*(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)]
+
+                                // repopulation rate (atoms flying in/out the laser beam)  in [1/s]
+                                const double gt=0.01/2 *(2*M_PI*1e6);
+                                // Natural linewidth  of the upper level [1/s]
+                                const double G=2*6 *(2*M_PI*1e6);
+
+                                // incoherent pumping rate from level |1> to |3> in [1/s]
+                                const double gp=2*.6 *(2*M_PI*1e6);
+
+                                // total decay of i-th level branching ratios. Rij branching of i-th level to j-th
+                                const double R31=0.5, R32=0.5;
+
+
+                                complex  E1c, E2c, E3c; // Complex conjugated Rabi frequencies
+
+                                complex  r21, r31, r32;  // density matrix elements
+                        ]]>
+                </globals>
+                <benchmark />
+    <arguments>
+                        <!-- Rabi frequency divided by 2 in [1/s] -->
+                        <!--probe-->
+      <argument name="E1o" type="real" default_value="0.0025*(2*M_PI*1e6)" />
+                        <!--pump fields-->
+      <argument name="E2o" type="real" default_value="6.0*(2*M_PI*1e6)" />
+      <argument name="E3o" type="real" default_value="0.0*(2*M_PI*1e6)" />
+                        <!-- Fields detuning in [1/s] -->
+                        <!-- probe field detuning-->
+      <argument name="d1"  type="real" default_value="0*(2*M_PI*1e6)" />
+                        <!-- averaged detuning of pump fields i.e. mid point -->
+      <argument name="da"  type="real" default_value="0*(2*M_PI*1e6)" />
+                        <!-- detuning of pump fields with respect to each other -->
+      <argument name="delta"  type="real" default_value=".001*(2*M_PI*1e6)" />
+    </arguments>
+                <bing />
+                <fftw plan="patient" />
+                <openmp />
+                <auto_vectorise />
+        </features>
+
+        <!-- 'z' and 't' to have dimensions [m] and [s]   -->
+        <geometry>
+                <propagation_dimension> z </propagation_dimension>
+                <transverse_dimensions>
+                        <dimension name="t"   lattice="1000"   domain="(-2.0e-6, 4.0e-6)" />
+                </transverse_dimensions>
+        </geometry>
+
+        <!-- Rabi frequency --> 
+        <vector name="E_field" type="complex" initial_space="t">
+                <components>E1 E2 E3</components>
+                <initialisation>
+                        <![CDATA[
+                        // Initial (at starting 'z' position) electromagnetic field does not depend on detuning
+                        // as well as time
+                        E1=E1o*exp(-pow( ((t-0.0)/1e-6),2) );
+                        E2=E2o;
+                        E3=E3o;
+                        ]]>
+                </initialisation>
+        </vector>
+
+        <vector name="density_matrix" type="complex" initial_space="t">
+                <components>r11 r22 r33 r12 r13  r23 </components>
+                <!--
+                                 note one of the level population is redundant since
+                                 r11+r22+r33=1
+                -->
+                <initialisation>
+                        <![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
+                        r11 = 1; r22 = 0; r33 = 0;
+                        r12 = 0; r13 = 0;
+                        r23 = 0;
+                        ]]>
+                </initialisation>
+        </vector>
+
+        <vector name="pump_detunings" type="complex" initial_space="t">
+                <components> d dc </components>
+                <!--dc is probably redundant since it is just complex conjugate of d-->
+                <initialisation>
+                  <![CDATA[
+                        d  = exp( i*t*delta );
+                        dc = conj(d);
+                  ]]>
+                </initialisation>
+        </vector>       
+
+
+        <sequence>
+                <!--For this set of conditions ARK45 is faster than ARK89-->
+                <integrate algorithm="ARK45" tolerance="1e-5" interval="7e-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>200 200</samples>
+                        <operators>
+        <operator kind="cross_propagation" algorithm="SI" propagation_dimension="t">
+                                        <integration_vectors>density_matrix</integration_vectors>
+          <dependencies>E_field pump_detunings</dependencies>
+          <boundary_condition kind="left">
+            <![CDATA[
+                                                        r11 = 1; r22 = 0; r33 = 0; 
+                                                        r12 = 0; r13 = 0; 
+                                                        r23 = 0; 
+            ]]>
+          </boundary_condition>
+                                        <![CDATA[
+                                                E1c = conj(E1);
+                                                E2c = conj(E2);
+                                                E3c = conj(E3);
+
+                                                r21=conj(r12);
+                                                r31=conj(r13);
+                                                r32=conj(r23);
+
+                                                // Equations of motions according to Simon's mathematica code
+                                                dr11_dt = gt - 2*(gp + gt)*r11 - E1*i*r13 + E1c*i*r31 + G*r33;
+                                                dr12_dt = (-gp - 2*gt - d1*i + da*i)*r12 - i*(E2*d + E3*dc)*r13 + E1c*i*r32;
+                                                dr13_dt = -(E1c*i*r11) - i*(E3c*d + E2c*dc)*r12 + (-G - gp - 2*gt - d1*i)*r13 + E1c*i*r33;
+                                                dr22_dt = gt - 2*gt*r22 - i*(E2*d + E3*dc)*r23 + i*(E3c*d + E2c*dc)*r32 + G*r33;
+                                                dr23_dt = -(E1c*i*r21) - i*(E3c*d + E2c*dc)*r22 + (-G - 2*gt - da*i)*r23 + i*(E3c*d + E2c*dc)*r33;
+                                                dr33_dt = 2*gp*r11 + E1*i*r13 + i*(E2*d + E3*dc)*r23 - E1c*i*r31 - i*(E3c*d + E2c*dc)*r32 - 2*(G + gt)*r33;
+
+                                        ]]>
+        </operator>
+                                <operator kind="ex" constant="yes">
+                                        <operator_names>Lt</operator_names>
+                                        <![CDATA[
+                                        Lt = i*1./c*kt;
+                                        ]]>
+                                </operator>
+        <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(r23) -Lt[E3] ;
+          ]]>
+                        </operators>
+                </integrate>
+        </sequence>
+
+
+
+
+        <!-- The output to generate -->
+        <output format="binary" filename="Nlevels_no_dopler_with_z.xsil">
+                <group>
+      <sampling basis="t(1000)" initial_sample="yes">
+                                <dependencies>E_field</dependencies>
+                                <moments>I1_out I2_out I3_out</moments>
+                                <![CDATA[
+                                I1_out = mod2(E1);
+                                I2_out = mod2(E2);
+                                I3_out = mod2(E3);
+                                ]]>
+                        </sampling>
+                </group>
+
+                <group>
+      <sampling basis="t(100)" initial_sample="yes">
+                                <dependencies>density_matrix</dependencies>
+                                <moments>
+                                        r11_out r22_out r33_out
+                                        r12_re_out r12_im_out r13_re_out r13_im_out
+                                                              r23_re_out r23_im_out
+                                </moments>
+                                <![CDATA[
+                                // populations output 
+                                r11_out = r11.Re();
+                                r22_out = r22.Re();
+                                r33_out = r33.Re();
+                                // coherences output 
+                                r12_re_out = r12.Re();
+                                r12_im_out = r12.Im();
+                                r13_re_out = r13.Re();
+                                r13_im_out = r13.Im();
+                                r23_re_out = r23.Re();
+                                r23_im_out = r23.Im();
+                                ]]>
+                        </sampling>
+                </group>
+        </output>
+
+
+<info>
+Script compiled with XMDS2 version 2.0 "Shiny!" (HEAD)
+See http://www.xmds.org for more information.
+
+Variables that can be specified on the command line:
+  Command line argument E1o = 1.570796e+04
+  Command line argument E2o = 3.769911e+07
+  Command line argument E3o = 0.000000e+00
+  Command line argument d1 = 0.000000e+00
+  Command line argument da = 0.000000e+00
+  Command line argument delta = 6.283185e+03
+</info>
+
+<XSIL Name="moment_group_1">
+  <Param Name="n_independent">2</Param>
+  <Array Name="variables" Type="Text">
+    <Dim>5</Dim>
+    <Stream><Metalink Format="Text" Delimiter=" \n"/>
+z t I1_out I2_out I3_out 
+    </Stream>
+  </Array>
+  <Array Name="data" Type="double">
+    <Dim>201</Dim>
+    <Dim>1000</Dim>
+    <Dim>5</Dim>
+    <Stream><Metalink Format="Binary" UnsignedLong="uint32" precision="double" Type="Remote" Encoding="LittleEndian"/>
+Nlevels_no_dopler_with_z_mg0.dat
+    </Stream>
+  </Array>
+</XSIL>
+
+<XSIL Name="moment_group_2">
+  <Param Name="n_independent">2</Param>
+  <Array Name="variables" Type="Text">
+    <Dim>11</Dim>
+    <Stream><Metalink Format="Text" Delimiter=" \n"/>
+z t r11_out r22_out r33_out r12_re_out r12_im_out r13_re_out r13_im_out r23_re_out r23_im_out 
+    </Stream>
+  </Array>
+  <Array Name="data" Type="double">
+    <Dim>201</Dim>
+    <Dim>100</Dim>
+    <Dim>11</Dim>
+    <Stream><Metalink Format="Binary" UnsignedLong="uint32" precision="double" Type="Remote" Encoding="LittleEndian"/>
+Nlevels_no_dopler_with_z_mg1.dat
+    </Stream>
+  </Array>
+</XSIL>
+</simulation>