Magneto-optical trapping forces for atoms and molecules with complex level structures

TL;DR

This paper analyzes how magneto-optical trapping forces depend on atomic and molecular level structures, revealing conditions for optimizing trapping strength and proposing improved polarization schemes for molecules like SrF.

Contribution

It provides a detailed theoretical analysis of the dependence of trapping forces on angular momenta and g-factors, and suggests strategies to enhance molecular MOT performance.

Findings

Trapping force depends on the sign of g_u but not g_l.

Zero g_u leads to no trapping force.

Reversing magnetic field and polarization can strengthen trapping.

Abstract

Laser cooling and magneto-optical trapping of molecules typically involves multiple transitions driven by several laser frequencies. We analyze how magneto-optical trapping forces depend on the angular momenta, $F_l$ and $F_u$, and the g-factors, $g_l$ and $g_u$, of the lower and upper states. When $F_l > F_u$ the polarizations must be reversed relative to cases where $F_u \ge F_l$. The correct choice of circular polarization depends on the sign of $g_{u}$ but not on the sign of $g_{l}$. If $g_{u}$ is zero there is no trapping force, and the trapping force is very weak whenever $g_u$ is small compared to $g_l$, which it usually is when the cooling transition is the $^{2}\Sigma$ to $^{2}\Pi_{1/2}$ transition of a molecule. For some molecules, mixing of the excited $^{2}\Pi_{1/2}$ state with a nearby $^{2}\Sigma$ excited state can greatly increase $g_u$, leading to stronger trapping forces. A strong trapping force can also be produced by rapidly and synchronously reversing both the magnetic field and the laser polarizations. We simulate a recent experiment on magneto-optical trapping of SrF molecules, and suggest that an alternative choice of laser beam polarizations will strengthen the trapping force.