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-rw-r--r--xmds2/Shahriar_system/Shahriar_system.xmds138
1 files changed, 66 insertions, 72 deletions
diff --git a/xmds2/Shahriar_system/Shahriar_system.xmds b/xmds2/Shahriar_system/Shahriar_system.xmds
index 0109168..0d30a32 100644
--- a/xmds2/Shahriar_system/Shahriar_system.xmds
+++ b/xmds2/Shahriar_system/Shahriar_system.xmds
@@ -3,30 +3,29 @@
<name>Shahriar_system</name>
- <author>Eugeniy Mikhailov</author>
- <author>Simon Rochester</author>
+ <author>Eugeniy Mikhailov, Simon Rochester</author>
<description>
License GPL.
- Solving 4 level atom in N-field configuration,
+ Solving 3 level atom in double drive configuration
+ after Shahriar paper about white cavity
with field propagation along spatial axis Z
- no Doppler broadening
+ no Doppler broadening.
- For master equations look "Four-level 'N-scheme' in bare and quasi-dressed states pictures"
- by T. Abi-Salloum, S. Meiselman, J.P. Davis and F.A. Narducci
- Journal of Modern Optics, 56: 18, 1926 -- 1932, (2009).
+ All fields detuned from upper level i.e. Raman configuration
- Present calculation matches Fig.3 (b) from the above paper.
- Note that I need to double all Rabi frequencies to match the figure.
- * -------- |4>
- * \
- * \ E3 -------- |3>
- * \ / \
- * \ E2 / \
- * \ / \ E1
- * ------- |2> \
- * \
+ *
+ * .....
+ * / ....
+ * / .... \
+ * / / \
+ * / /-------- |3>
+ * E3 / \
+ * / E2 \
+ * / / \ E1
+ * ------ |2> \
+ * \
* ------- |1>
*
@@ -55,30 +54,36 @@
// 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 j's level in [1/s]
- const double G3=2*2.7 *(2*M_PI*1e6);
- const double G4=2*3.0 *(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*.0 *(2*M_PI*1e6);
// 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 E1c, E2c, E3c; // Complex conjugated Rabi frequencies
- complex r21, r31, r41, r32, r42, r43, r44; // density matrix elements
+ 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)" />
- <argument name="E2o" type="real" default_value="6*(2*M_PI*1e6)" />
- <argument name="E3o" type="real" default_value="0.0*(2*M_PI*1e6)" />
+ <!--pump fields-->
+ <argument name="E2o" type="real" default_value="1.0*(2*M_PI*1e6)" />
+ <argument name="E3o" type="real" default_value="1.0*(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" />
+ <!-- probe field detuning-->
+ <argument name="d1" type="real" default_value="12*(2*M_PI*1e6)" />
+ <!-- averaged detuning of pump fields i.e. mid point -->
+ <argument name="da" type="real" default_value="12*(2*M_PI*1e6)" />
+ <!-- detuning of pump fields with respect to each other -->
+ <argument name="delta" type="real" default_value="6*(2*M_PI*1e6)" />
</arguments>
<bing />
<fftw plan="patient" />
@@ -109,13 +114,10 @@
</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>
+ <components>r11 r22 r33 r12 r13 r23 </components>
<!--
note one of the level population is redundant since
- r11+r22+r33+r44=1
- so r11 is missing
+ r11+r22+r33=1
-->
<initialisation>
<![CDATA[
@@ -128,17 +130,28 @@
// 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;
+ 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">
+ <integrate algorithm="ARK45" tolerance="1e-5" interval="4e-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-->
@@ -147,13 +160,12 @@
<operators>
<operator kind="cross_propagation" algorithm="SI" propagation_dimension="t">
<integration_vectors>density_matrix</integration_vectors>
- <dependencies>E_field</dependencies>
+ <dependencies>E_field pump_detunings</dependencies>
<boundary_condition kind="left">
<![CDATA[
- r11 = 1; r22 = 0; r33 = 0; r44 = 0;
- r12 = 0; r13 = 0; r14 = 0;
- r23 = 0; r24 = 0;
- r34 = 0;
+ r11 = 1; r22 = 0; r33 = 0;
+ r12 = 0; r13 = 0;
+ r23 = 0;
]]>
</boundary_condition>
<![CDATA[
@@ -163,23 +175,16 @@
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 + G3*r33*R31 + G4*r44*R41 + i*(-(E1*r13) + E1c*r31);
- dr12_dt = -(gt*r12) + i*((-delta1 + delta2)*r12 - E2*r13 - E3*r14 + E1c*r32);
- dr13_dt = -((G3 + 2*gt)*r13)/2. + i*(-(delta1*r13) - E1c*r11 - E2c*r12 + E1c*r33);
- dr14_dt = -((G4 + 2*gt)*r14)/2. + i*(-((delta1 - delta2 + delta3)*r14) - E3c*r12 + E1c*r34);
- dr22_dt = gt/2. - gt*r22 + G3*r33*R32 + G4*r44*R42 + i*(-(E2*r23) - E3*r24 + E2c*r32 + E3c*r42);
- dr23_dt = -((G3 + 2*gt)*r23)/2. + i*(-(delta2*r23) - E1c*r21 - E2c*r22 + E2c*r33 + E3c*r43);
- dr24_dt = -((G4 + 2*gt)*r24)/2. + i*(-(delta3*r24) - E3c*r22 + E2c*r34 + E3c*r44);
- dr33_dt = -((G3 + gt)*r33) + i*(E1*r13 + E2*r23 - E1c*r31 - E2c*r32);
- dr34_dt = -((G3 + G4 + 2*gt)*r34)/2. + i*((delta2 - delta3)*r34 + E1*r14 + E2*r24 - E3c*r32);
- dr44_dt = -((G4 + gt)*r44) + i*(E3*r24 - E3c*r42);
+ 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">
@@ -193,17 +198,14 @@
<![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] ;
+ 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">
+ <output format="binary" filename="Shahriar_system.xsil">
<group>
<sampling basis="t(1000)" initial_sample="yes">
<dependencies>E_field</dependencies>
@@ -220,30 +222,22 @@
<sampling basis="t(100)" initial_sample="yes">
<dependencies>density_matrix</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
+ 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();
- r44_out = r44.Re();
// coherences output
r12_re_out = r12.Re();
r12_im_out = r12.Im();
r13_re_out = r13.Re();
r13_im_out = r13.Im();
- r14_re_out = r14.Re();
- r14_im_out = r14.Im();
r23_re_out = r23.Re();
r23_im_out = r23.Im();
- r24_re_out = r24.Re();
- r24_im_out = r24.Im();
- r34_re_out = r34.Re();
- r34_im_out = r34.Im();
]]>
</sampling>
</group>
generated by cgit v1.2.3 (git 2.39.1) at 2024-11-16 16:07:03 +0000