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authorSimon Rochester <simon.rochester@gmail.com>2011-08-21 17:33:33 -0700
committerSimon Rochester <simon.rochester@gmail.com>2011-08-21 17:33:33 -0700
commita6dad51ad585a235dc7bfe89ba1b488037642b9a (patch)
treed60db3823edd86316eb3dda562c53e5714b638cf /xmds2
parent04cb902513d09f3d762bf65bc87c521b0497b08a (diff)
downloadNresonances-a6dad51ad585a235dc7bfe89ba1b488037642b9a.tar.gz
Nresonances-a6dad51ad585a235dc7bfe89ba1b488037642b9a.zip
xmds2 model of Gena's 4-level system.
GenerateGenasSystem.nb: generate evolution equations GenasSystemPlots: code for reading output data, converting complex field amplitudes to rotation angle/ellipticity, and plotting
Diffstat (limited to 'xmds2')
-rwxr-xr-xxmds2/Genas_system/GenasSystemPlots.nb458
-rwxr-xr-xxmds2/Genas_system/Genas_system.xmds218
-rwxr-xr-xxmds2/Genas_system/GenerateGenasSystem.nb2722
-rwxr-xr-xxmds2/Genas_system/Makefile37
4 files changed, 3435 insertions, 0 deletions
diff --git a/xmds2/Genas_system/GenasSystemPlots.nb b/xmds2/Genas_system/GenasSystemPlots.nb
new file mode 100755
index 0000000..c347101
--- /dev/null
+++ b/xmds2/Genas_system/GenasSystemPlots.nb
@@ -0,0 +1,458 @@
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diff --git a/xmds2/Genas_system/Genas_system.xmds b/xmds2/Genas_system/Genas_system.xmds
new file mode 100755
index 0000000..e855e4f
--- /dev/null
+++ b/xmds2/Genas_system/Genas_system.xmds
@@ -0,0 +1,218 @@
+<?xml version="1.0"?>
+<simulation xmds-version="2">
+
+ <name>Genas_system</name>
+
+ <author>Eugeniy Mikhailov and Simon Rochester</author>
+ <description>
+ License GPL.
+
+ Solving 4 level atom in 0->1 configuration,
+ with field propagation along spatial axis Z
+ no Doppler broadening
+
+ 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=1e6*(1e6); //number of particles per cubic m i.e. density
+ const double Gamma=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/16.0/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*M_PI*1e6);
+ // Natural linewidth of upper state in [1/s]
+ const double g0=1.*(2*M_PI*1e6);
+
+ complex Exc, Eyc; // Complex-conjugated Rabi frequency
+
+ complex r21, r31, r41, r32, r42, r43, r44; // density matrix elements
+ ]]>
+ </globals>
+ <benchmark />
+ <arguments>
+ <!-- Real and imaginary parts of complex Rabi frequency in [1/s] -->
+ <argument name="ExReo" type="real" default_value="(3.+0.001)*(2*M_PI*1.e6)" />
+ <argument name="ExImo" type="real" default_value="0." />
+ <argument name="EyReo" type="real" default_value="0." />
+ <argument name="EyImo" type="real" default_value="(3.-0.001)*(2*M_PI*1.e6)" />
+ <!-- light detuning in [1/s] -->
+ <argument name="delta" type="real" default_value="3.0*(2*M_PI*1e6)" />
+ <!--shift of upper-state M=0 sublevel-->
+ <argument name="delta0" type="real" default_value="1.*(2*M_PI*1e6)" />
+ <!--Static B-field Larmor frequency-->
+ <argument name="OL" type="real" default_value="4.*(2*M_PI*1e6)" />
+ <!--rf Rabi frequency-->
+ <argument name="Orf" type="real" default_value="0.1*(2*M_PI*1e6)" />
+ <!--rf frequency-->
+ <argument name="orf" type="real" default_value="4.*(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="(-1.5e-7, 2.5e-7)" />
+ </transverse_dimensions>
+ </geometry>
+
+ <!-- Rabi frequency -->
+ <vector name="E_field" type="complex" initial_space="t">
+ <components>Ex Ey</components>
+ <initialisation>
+ <![CDATA[
+ // Initial (at starting 'z' position) electromagnetic field does not depend on detuning
+ // as well as time
+ Ex=(ExReo+i*ExImo)*exp(-pow( ((t-0.0)/1e-7),2) );
+ Ey=(EyReo+i*EyImo)*exp(-pow( ((t-0.0)/1e-7),2) );
+ ]]>
+ </initialisation>
+ </vector>
+
+ <vector name="density_matrix" type="complex" initial_space="t">
+ <components>r11 r22 r33 r12 r13 r14 r23 r24 r34 r44</components>
+ <initialisation>
+ <![CDATA[
+ r11 = 1; r22 = 0; r33 = 0; r44 = 0;
+ r12 = 0; r13 = 0; r14 = 0;
+ r23 = 0; r24 = 0;
+ r34 = 0;
+ ]]>
+ </initialisation>
+ </vector>
+
+ <vector name="rfField" type="real">
+ <components> rf </components>
+ <initialisation>
+ <![CDATA[
+ rf = Orf*sin(orf*t);
+ ]]>
+ </initialisation>
+ </vector>
+
+ <sequence>
+ <integrate algorithm="ARK45" tolerance="0.05e-7" interval="1e1">
+ <samples>200 200</samples>
+ <operators>
+ <operator kind="cross_propagation" algorithm="SI" propagation_dimension="t">
+ <integration_vectors>density_matrix</integration_vectors>
+ <dependencies>E_field rfField</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;
+ ]]>
+ </boundary_condition>
+ <![CDATA[
+ Exc = conj(Ex);
+ Eyc = conj(Ey);
+
+ r21=conj(r12);
+ r31=conj(r13);
+ r41=conj(r14);
+ r32=conj(r23);
+ r42=conj(r24);
+ r43=conj(r34);
+
+ // Equations of motions according to Simon's mathematica code
+ dr11_dt = gt - gt*r11 + (-Ey - Ex*i)*r12 + i*(Ex + Ey*i)*r14 + i*(Exc + Eyc*i)*r21 + (-Eyc - Exc*i)*r41 + g0*(r22 + r33 + r44);
+ dr12_dt = (2*(Eyc - Exc*i)*r11 - i*((2*delta - (g0 + 2*gt)*i - 2*OL - 2*rf)*r12 - 2*(Exc + Eyc*i)*r22 + 2*(Exc - Eyc*i)*r42))/2.;
+ dr13_dt = (-g0/2. - gt - delta*i + delta0*i)*r13 + i*(Exc + Eyc*i)*r23 + (-Eyc - Exc*i)*r43;
+ dr14_dt = -(i*((2*delta - (g0 + 2*gt)*i + 2*OL + 2*rf)*r14 - 2*(Exc + Eyc*i)*r24 - 2*(Exc - Eyc*i)*(r11 - r44)))/2.;
+ dr22_dt = (Ey + Ex*i)*r12 + (Eyc - Exc*i)*r21 - (g0 + gt)*r22;
+ dr23_dt = (Ey + Ex*i)*r13 + i*(delta0 + i*(g0 + gt + i*OL) - rf)*r23;
+ dr24_dt = (Ey + Ex*i)*r14 + (Eyc + Exc*i)*r21 - (g0 + gt + 2*i*OL + 2*i*rf)*r24;
+ dr33_dt = -((g0 + gt)*r33);
+ dr34_dt = (Eyc + Exc*i)*r31 - i*(delta0 - (g0 + gt)*i + OL + rf)*r34;
+ dr44_dt = (Ey - Ex*i)*r14 + (Eyc + Exc*i)*r41 - (g0 + gt)*r44;
+ ]]>
+ </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[
+ dEx_dz = i*eta*conj(r12-r14) - Lt[Ex] ;
+ dEy_dz = -eta*conj(r12+r14) - Lt[Ey] ;
+ ]]>
+ </operators>
+ </integrate>
+ </sequence>
+
+ <!-- The output to generate -->
+ <output format="binary" filename="Genas_system.xsil">
+ <group>
+ <sampling basis="t(100)" initial_sample="yes">
+ <dependencies>E_field</dependencies>
+ <moments>Ex_re_out Ex_im_out Ey_re_out Ey_im_out</moments>
+ <![CDATA[
+ Ex_re_out = Ex.Re();
+ Ex_im_out = Ex.Im();
+ Ey_re_out = Ey.Re();
+ Ey_im_out = Ey.Im();
+ ]]>
+ </sampling>
+ </group>
+
+ <group>
+ <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
+ </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>
+ </output>
+</simulation>
+
+<!--
+vim: ts=2 sw=2 foldmethod=indent:
+-->
diff --git a/xmds2/Genas_system/GenerateGenasSystem.nb b/xmds2/Genas_system/GenerateGenasSystem.nb
new file mode 100755
index 0000000..ab9069b
--- /dev/null
+++ b/xmds2/Genas_system/GenerateGenasSystem.nb
@@ -0,0 +1,2722 @@
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diff --git a/xmds2/Genas_system/Makefile b/xmds2/Genas_system/Makefile
new file mode 100755
index 0000000..0e82991
--- /dev/null
+++ b/xmds2/Genas_system/Makefile
@@ -0,0 +1,37 @@
+### -*- make -*-
+### This file is part of the Debian xmds package
+### Copyright (C) 2006 Rafael Laboissiere
+### This file is relased under the GNU General Public License
+### NO WARRANTIES!
+
+### This makefile can be used to build and run the XMDS examples
+
+XMDS_FILES = $(shell ls *.xmds)
+RUN_FILES = $(patsubst %.xmds,%.run,$(XMDS_FILES))
+CC_FILES = $(patsubst %.xmds,%.cc,$(XMDS_FILES))
+XSIL_FILES = $(patsubst %.xmds,%.xsil,$(XMDS_FILES))
+M_FILES = $(patsubst %.xmds,%.m,$(XMDS_FILES))
+
+XMDS = xmds2
+XSIL2GRAPHICS = xsil2graphics2
+
+all: $(M_FILES)
+
+%.run: %.xmds
+ $(XMDS) $<
+ mv $(patsubst %.xmds,%,$<) $@
+
+%.xsil: %.run
+ ./$<
+
+%.m: %.xsil
+ $(XSIL2GRAPHICS) -e $<
+
+plot: $(M_FILES)
+ octave pp.m
+
+clean:
+ rm -f $(CC_FILES) $(RUN_FILES) $(M_FILES) $(XSIL_FILES) *.wisdom.fftw3 *.dat octave-core *.wisdom *.pdf
+
+.PRECIOUS: %.run %.xsil %.m
+.PHONY: all clean
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