realistic_Rb
Eugeniy Mikhailov
License GPL.
Solving simplified Rb atom model
with fields propagation along spatial axis Z
with Doppler broadening.
We assume four-wave mixing condition when w3-w4=w2-w1 i.e. fields E3 and E4 drive the same
resonance as fields E2 and E1.
* --------------- | F=1, 2P_3/2 >
* \ \
* \ E3_r \ -------- | F=2, 2P_+1/2 >
* \ E4_r \ / \
* \ \ / E2_l \
* \ / \ E1_l
* | F=2, 2S_1/2 > -------------- \
* \ \
* \ \
* ------------- | F=1, 2S_1/2 >
*
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
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 G3=3.0 *(2*M_PI*1e6);
const double G4=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 E1ac, E2ac, E3ac, E4ac; // Complex conjugated Rabi frequencies
complex r21, r31, r41, r32, r42, r43, r44; // density matrix elements
// 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
E1 E2 E3 E4
probability_v
probability_v_norm
Maxwell_distribution_probabilities
E1a E2a E3a E4a
E_field Maxwell_distribution_probabilities Maxwell_distribution_probabilities_norm
r11a r22a r33a r12a r13a r14a r23a r24a r34a r44a
density_matrix Maxwell_distribution_probabilities Maxwell_distribution_probabilities_norm
r11 r22 r33 r12 r13 r14 r23 r24 r34 r44
E_field_avgd
100 100
density_matrix
E_field_avgd
Lt
E_field
density_matrix