Optical pumping of dense vapors is limited by radiation trapping, in which the scattered (and generally unpolarized) light gets reabsorbed before leaving the vapor.
This Monte Carlo simulation of the process is adapted from my thesis, which involved spin exchange optical pumping. The main insight was to detune the laser frequency away from the center of the atomic resonance line, whose shape is a Voigt profile. Only atoms whose velocity Doppler shifts them into resonance are likely to absorb the detuned photon, and will scatter it with a frequency distribution centered at the original detuning. This reduces the likelihood of reabsorption, achieving a higher polarization in a denser vapor and facilitating spin exchange.
In the simulation, a circularly polarized laser beam enters a cylindrical cell containing an alkali vapor. Each incident photon scatters one or more times, and eventually escapes from the cell. Its total spin angular momentum transfer ΔJz is +⅓ for the initial scatter, but may be negative after multiple scatters. The equilibrium polarization is where <ΔJz> = 0.
You may specify the alkali vapor (K, Rb, Cs), its polarization and temperature, and the frequency detuning of the laser. The vapor concentration and resulting optical depth of the cell increase nonlinearly with temperature.
You may run the simulation at different speeds: Run for continuously, One Photon to pause after each incident photon escapes, and One Scatter to pause after each scatter. Pause pauses the simulation, and Reset clears the statistics (as does changing the input values).
For now, it displays the trajectory, ΔJz, and the number of scatters for the current photon, and the mean value and probability density of these quantities across all photons.
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