Optical pumping model of the polarization for the TRINAT experiment

The TRIUMF Neutral Atom Trap (TRINAT) has an active experimental program to measure angular correlations in the decay of spin-polarized K. An overview of our recent progress including a successful run in December 2012 is described in our other report. This report will focus on our progress in developing a better model of the optical-pumping process that polarizes the trapped atoms. Optical pumping uses circularly polarized laser light to drive the potassium atoms' single valence electron to an extreme Zeeman sublevel which, due to the hyperfine coupling of atomic and nuclear angular momenta, corresponds to complete atomic and nuclear polarization. An atom in a ground state absorbs a circularly polarized photon, which promotes it to an excited state and imparts an additional unit of angular momentum to the atom. Once in the excited state, the atom quickly decays; the emitted photon can have any polarization. Through a series of repeated absorptions and emissions, the atom undergoes a biased random walk to an extreme sublevel. Once in this sublevel, called the stretched state, the atom can no longer absorb a photon as there is no excited state with the appropriate quantum numbers to conserve angular momentum. A schematic diagram of this process is shown in the Fig.1. Once an atom reaches the stretched state, it is both trapped in that state and completely polarized, an ideal combination for our polarized decay studies.