Shahriar_system
Eugeniy Mikhailov, Simon Rochester
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.
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
]]>
z
E1 E2 E3
r11 r22 r33 r12 r13 r23
// 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;
]]>
d dc
200 200
density_matrix
E_field pump_detunings
Lt
E_field
density_matrix
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
2
5
z t I1_out I2_out I3_out
201
1000
5
Nlevels_no_dopler_with_z_mg0.dat
2
11
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
201
100
11
Nlevels_no_dopler_with_z_mg1.dat