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>
*
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
IMPORTANT simplification: E2 = E3 by magnitude then we can use a field consisting
of beat note between E1 and E2 oscillating at frequency wa=(w1+w2)/2
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
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.
z
E1 Ef
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;
]]>
200 200
density_matrix
E_field
Lt
E_field
density_matrix