From 97ae63ce4cff3c1ee6f8caf2a52271acac7ea00f Mon Sep 17 00:00:00 2001
From: evmik <evgmik@gmail.com>
Date: Fri, 27 May 2011 15:50:54 -0400
Subject: add solver generated by mathematica

---
 .../Nlevels_no_dopler_no_z_from_mathematica.xmds   | 174 +++++++++++++++++++++
 1 file changed, 174 insertions(+)
 create mode 100644 xmds2/Nlevels_no_dopler_no_z.example/Nlevels_no_dopler_no_z_from_mathematica.xmds

diff --git a/xmds2/Nlevels_no_dopler_no_z.example/Nlevels_no_dopler_no_z_from_mathematica.xmds b/xmds2/Nlevels_no_dopler_no_z.example/Nlevels_no_dopler_no_z_from_mathematica.xmds
new file mode 100644
index 0000000..d98d514
--- /dev/null
+++ b/xmds2/Nlevels_no_dopler_no_z.example/Nlevels_no_dopler_no_z_from_mathematica.xmds
@@ -0,0 +1,174 @@
+<?xml version="1.0"?>
+<simulation xmds-version="2">
+
+	<name>Nlevels_no_dopler_no_z_from_mathematica</name>
+
+	<author>Eugeniy Mikhailov</author>
+	<description>
+		License GPL.
+
+		Solving 4 level atom in N-field configuration,
+		no field propagation along spatial axis included
+		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).
+
+		Present calculation matches Fig.3 (b) from the above paper. 
+		Note that I need to double all Rabi frequencies to match the figure.
+
+		*  -------- |4>
+		*    \        
+		*     \ Ec    -------- |3>  
+		*      \       /    \
+		*       \  E2 /      \ 
+		*        \   /        \ E1
+		*       ------- |2>    \
+		*                       \
+		*                    ------- |1>
+		*
+
+		We moved to dimensionless units
+		t -> t*g    ,time
+		z -> z*g/c  , distance
+		rabi_frequency -> rabi_frequency/g 
+		eta -> eta*c/g^2      , coupling constant
+		gij -> gij/g
+		Wij -> Wij/g
+
+		where g is 1MHz rate
+	</description>
+
+	<features>
+		<benchmark />
+		<bing />
+		<fftw plan="patient" />
+		<openmp />
+		<auto_vectorise />
+		<globals>
+			<![CDATA[
+			// repopulation rate (atoms flying in/out the laser beam)  in MHz
+			const double gt=0.01/2;
+			// Natural linewidth  of j's level in MHz
+			const double G3=2.7;
+			const double G4=3.0;
+
+			// branching ratios
+			const double R41=0.0, R42=1;
+			const double R31=0.5, R32=0.5;
+
+			// const double d1=0;         // E2 detuning in MHz
+			const double d2=0;         // E2 detuning in MHz
+			const double d3=0;         // Ec detuning in MHz
+
+			const complex E1=0.005/2;     // Rabi frequency in MHz
+			const complex E2=5.0/2;         // Rabi frequency in MHz
+			const complex Ec=6.0/2;         // Rabi frequency in MHz
+
+			complex  E1c, E2c, Ecc; // Complex conjugated Rabi frequencies
+
+			//complex  r21, r31, r41, r32, r42, r43;
+
+			]]>
+		</globals>
+	</features>
+
+	<geometry>
+		<propagation_dimension> t </propagation_dimension>
+		<transverse_dimensions>
+			<dimension name="d1" lattice="1280"  domain="(-60, 60)" />
+		</transverse_dimensions>
+	</geometry>
+
+	<vector name="density_matrix" type="complex" dimensions="d1">
+		<components>r11 r22 r33 r44 r12 r13 r14 r23 r24 r34   r21 r31 r41 r32 r42 r43</components>
+		<!--
+				 note one of the level population is redundant since
+				 r11+r22+r33+r44=1
+				 so r11 is missing
+		-->
+		<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 incriment 
+			// seems to be huge and adaptive solver makes smaller and smaller steps.
+			// As quicj and dirty fix I reshufle initial poulation  
+			// 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
+			r22 = 0.001; r33 = 0; r44 = 0;
+			r12 = 0; r13 = 0; r14 = 0;
+			r23 = 0; r24 = 0;
+			r34 = 0;
+			]]>
+		</initialisation>
+	</vector>
+
+	<sequence>
+		<integrate algorithm="ARK45" interval="600" tolerance="1e-3">
+			<samples>128</samples>
+			<operators>
+				<integration_vectors>density_matrix</integration_vectors>
+				<![CDATA[
+				E1c = conj(E1);
+				E2c = conj(E2);
+				Ecc = conj(Ec);
+
+				// r21=conj(r12);
+				// r31=conj(r13);
+				// r41=conj(r14);
+				// r32=conj(r23);
+				// r42=conj(r24);
+				// r43=conj(r34);
+
+				// Equations of motions see page 1928 of the Frank's JMO paper
+				dr11_dt = gt - 2*gt*r11 + E1*i*(-r13 + r31) + 2*G3*r33*R31 + 2*G4*r44*R41;
+				dr12_dt = -2*gt*r12 + i*((-d1 + d2)*r12 - E2*r13 - Ec*r14 + E1*r32);
+				dr13_dt = -((G3 + 2*gt)*r13) + i*(-(E1*r11) - E2*r12 - d1*r13 + E1*r33);
+				dr14_dt = -((G4 + 2*gt)*r14) + i*(-(Ec*r12) - (d1 - d2 + d3)*r14 + E1*r34);
+				dr21_dt = -2*gt*r21 + i*((d1 - d2)*r21 - E1*r23 + E2*r31 + Ec*r41);
+				dr22_dt = gt - 2*gt*r22 + i*(-(E2*r23) - Ec*r24 + E2*r32 + Ec*r42) + 2*G3*r33*R32 + 2*G4*r44*R42;
+				dr23_dt = -((G3 + 2*gt)*r23) + i*(-(E1*r21) - E2*r22 - d2*r23 + E2*r33 + Ec*r43);
+				dr24_dt = -((G4 + 2*gt)*r24) + i*(-(Ec*r22) - d3*r24 + E2*r34 + Ec*r44);
+				dr31_dt = -((G3 + 2*gt)*r31) + i*(E1*r11 + E2*r21 + d1*r31 - E1*r33);
+				dr32_dt = -((G3 + 2*gt)*r32) + i*(E1*r12 + E2*r22 + d2*r32 - E2*r33 - Ec*r34);
+				dr33_dt = i*(E1*r13 + E2*r23 - E1*r31 - E2*r32) - 2*(G3 + gt)*r33;
+				dr34_dt = -((G3 + G4 + 2*gt)*r34) + i*(E1*r14 + E2*r24 - Ec*r32 + (d2 - d3)*r34);
+				dr41_dt = -((G4 + 2*gt)*r41) + i*(Ec*r21 + (d1 - d2 + d3)*r41 - E1*r43);
+				dr42_dt = -((G4 + 2*gt)*r42) + i*(Ec*r22 + d3*r42 - E2*r43 - Ec*r44);
+				dr43_dt = -((G3 + G4 + 2*gt)*r43) + i*(Ec*r23 - E1*r41 - E2*r42 + (-d2 + d3)*r43);
+				dr44_dt = Ec*i*(r24 - r42) - 2*(G4 + gt)*r44;
+				]]>
+			</operators>
+		</integrate>
+	</sequence>
+
+
+
+
+	<!-- The output to generate -->
+	<output format="binary" filename="Nlevels_no_dopler_no_z_from_mathematica.xsil">
+		<group>
+			<sampling basis="d1" initial_sample="yes">
+				<dependencies>density_matrix</dependencies>
+				<moments>>r13_rlOut r13_imOut >r23_rlOut r23_imOut r24_rlOut r24_imOut</moments>
+				<![CDATA[
+				r13_rlOut = r13.Re();
+				r13_imOut = r13.Im();
+				r23_rlOut = r23.Re();
+				r23_imOut = r23.Im();
+				r24_rlOut = r24.Re();
+				r24_imOut = r24.Im();
+				]]>
+			</sampling>
+		</group>
+	</output>
+
+</simulation>
+	
+<!-- 
+vim: ts=2 sw=2 foldmethod=indent: 
+-->
-- 
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