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| -rw-r--r-- | xmds2/Shahriar_system/Makefile | 37 | ||||
| -rw-r--r-- | xmds2/Shahriar_system/Shahriar_system.xmds | 256 |
2 files changed, 293 insertions, 0 deletions
diff --git a/xmds2/Shahriar_system/Makefile b/xmds2/Shahriar_system/Makefile new file mode 100644 index 0000000..a89800a --- /dev/null +++ b/xmds2/Shahriar_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 = xsil2graphics + +all: $(M_FILES) + +%.run: %.xmds + $(XMDS) $< + mv $(patsubst %.xmds,%,$<) $@ + +%.xsil: %.run + ./$< + +%.m: %.xsil + $(XSIL2GRAPHICS) $< + +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 diff --git a/xmds2/Shahriar_system/Shahriar_system.xmds b/xmds2/Shahriar_system/Shahriar_system.xmds new file mode 100644 index 0000000..0109168 --- /dev/null +++ b/xmds2/Shahriar_system/Shahriar_system.xmds @@ -0,0 +1,256 @@ +<?xml version="1.0"?> +<simulation xmds-version="2"> + + <name>Shahriar_system</name> + + <author>Eugeniy Mikhailov</author> + <author>Simon Rochester</author> + <description> + License GPL. + + Solving 4 level atom in N-field configuration, + with field propagation along spatial axis Z + 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> + * \ + * \ E3 -------- |3> + * \ / \ + * \ 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 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); + + // 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 + ]]> + </globals> + <benchmark /> + <arguments> + <!-- Rabi frequency divided by 2 in [1/s] --> + <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)" /> + <!-- 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" /> + </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 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> + <!-- + 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 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; r44 = 0; + r12 = 0; r13 = 0; r14 = 0; + r23 = 0; r24 = 0; + r34 = 0; + ]]> + </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</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[ + E1c = conj(E1); + E2c = conj(E2); + E3c = conj(E3); + + 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); + ]]> + </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(r24) -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 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: +--> |