The optical pumping process is quite completed for 7Li atoms especially its D2 transition, due to the nature that hyperfine levels of excited state 2P3/2 is poorly resolved. Most times people treat it as a single level, but in situations when specific ground magnetic sublevel is desired, a careful engineer of laser parameters has to be choosen. Since analytic solution is quite complicated, simulation provides good guidline about what's going on under three-level-transition.

Although the quantum transition of atoms (especially alkali atoms has been well studied by quantum mechanics, the accurate analytical solution of optical pumping process under certain conditions is very much rely on 2-level system model, in which the population of involved quantum states ( usually noted as ground state and excited state) is descriped by Optical Bloch equations.

However, apart from the ideal case of a two-level cycling transition, more general situation is that people has to deal with multi-level atoms systems, where atoms have chance to go into dark states and thus breke the assumptions of Optical Bloch equations. Most importantly, 3-level-system is of importance in atomic physics. Alkali atoms have well documented transition strength of hyperfine (hpf) states and are widely used in cold atoms physics when combining other good properities. As in our research, Lithium 7 atom is being used to approach super large BEC(Bose-Einstein Condensate), well understand the behavior of Li7 atom under optical pumpuing is necessary.

Above shown is the D line transitions of the two main lithium isotopes. This study will focus on the element Li7. The D1 line excited state of Li7 is not well resolved due to that fact that their seperation is much smaller than natrual linewidth, so effectively its a single level but with hiden states. In comparison, the D1 line of Li 7 excited state is well seperated and thus has to be trated individually. This simulation is to study the dynamics os population transfer of the magnetic sublevels of hpf states under different laser frequency, polarization, intensity, etc.

The change of hpf states magnetic sublevels are limited to selsection rules, the Delta_F = 0, +1, -1;
Delta_m = 0, +1, -1;
when Delta_F = 0, only Delta_m = +1, -1 are allowd

This simulation is based on the Optical Bloch equations for two level system, modified and extened it to multi-level systems in lithium.