Nlevels_with_MOR
Eugeniy Mikhailov, M. Guidry
License GPL.
Solving split 3-level atom
with field propagation along spatial axis Z
with Doppler broadening.
*
* -------- |a>
* / / \ \
* EdL / / \ \
* / / \ \
* |c> ----------/--- \ \ EpR
* / EpL \ \
* |C> -------------- \ \
* EdR \ \
* \ \
* ------\------ |b>
* \
* ------------- |B>
*
*
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
the upper level decay rate in the same units as Rabi frequency.
section
double eta = 0; // eta constant in the wave equation for Rabi frequency. Units are [1/(m s)]
// --------- Atom and cell properties -------------------------
// range of Maxwell distribution atomic velocities
const double mass = (86.909180527 * 1.660538921e-27); // atom mass in [kg]
// above mass expression is written as (expression is isotopic_mass * atomic_mass_unit)
// Average sqrt(v^2) in Maxwell distribution for one dimension
// Maxwell related parameters will be calculated in section
double v_thermal_averaged=0;
// Maxwell distribution velocities range to take in account in [m/s]
double V_maxwell_min = 0, V_maxwell_max = 0;
// repopulation rate (atoms flying in/out the laser beam) in [1/s]
//const double gt=0.01 *(2*M_PI*1e6);
// Natural linewidth of j's level in [1/s]
//const double Ga=3.0 *(2*M_PI*1e6);
//const double G4=3.0 *(2*M_PI*1e6);
complex g = Gamma_super;
complex gbc = (2*M_PI)*1e3; // 1/s untits
const complex Split = 0;
const complex noise = 0;
complex Gab, GAB, Gca, GCA, Gcb, GCB;
// total decay of i-th level branching ratios. Rij branching of i-th level to j-th
//const double Rab=0.5, Rac=0.5;
complex EdLac, EdRac, EpLac, EpRac;
// inner use variables
double probability_v; // will be used as p(v) in Maxwell distribution
]]>
0 to provide range for Maxwell velocity distribution\n");
v_thermal_averaged=sqrt(k_boltzmann*Temperature/mass);
// Maxwell distribution velocities range to take in account in [m/s]
// there is almost zero probability for higher velocity p(4*v_av) = 3.3e-04 * p(0)
V_maxwell_min = -4*v_thermal_averaged; V_maxwell_max = -V_maxwell_min;
// eta constant in the wave equation for Rabi frequency. Units are [1/(m s)]
eta = 3*lambda*lambda*Ndens*Gamma_super/8.0/M_PI;
]]>
z
EdL EdR EpL EpR
probability_v
probability_v_norm
Maxwell_distribution_probabilities
EdLa EdRa EpLa EpRa
E_field Maxwell_distribution_probabilities Maxwell_distribution_probabilities_norm
rbb_av rBB_av rcc_av rCC_av raa_av rcb_av rab_av rca_av rCB_av rAB_av rCA_av
density_matrix Maxwell_distribution_probabilities Maxwell_distribution_probabilities_norm
rbb rBB rcc rCC raa rcb rab rca rCB rAB rCA
E_field_avgd
100 100
density_matrix
E_field_avgd
Lt
E_field
density_matrix