Development of coherent transient techniques for measurements of atomic g-factor ratios

We have developed two coherent transient techniques for investigations into precision measurements of atomic g-factor ratios that utilize laser cooled atoms. The first technique involves excitation of coherence gratings involving magnetic sublevels of a single ground state in Rb using two traveling wave laser pulses with orthogonal polarizations. To understand this technique, we have developed a theoretical formalism using rotation matrices that describes the evolution of coherences in the presence of a magnetic field along an arbitrary direction. Theoretical predictions for the functional form of Larmor oscillations in a magnetic field are studied using a coherent transient effect known as magnetic grating free induction decay (MGFID) in room temperature vapour and laser cooled atoms. We find the predictions to be in excellent agreement with data. By using rate equations to model atomic coherences, it is also possible to predict the evolution of magnetic grating echoes (MGE) in a magnetic field. We compare these predictions with experiments from cold atoms. Although Larmor oscillation in the MGFID could be used for measurements of atomic g-factor ratios, considerations of probe power requirements and systematic effects due to the ac-Stark shift show that another (atomic magnetometry) technique is more suitable.;Using the atomic magnetometry technique, we demonstrate measurements of the ratio of Larmor oscillations from coherences between magnetic sublevels in the ground states of 85Rb and 87Rb atoms confined in a dual-isotope magneto-optical trap. The two isotopes are exposed to the same constant magnetic field, and Larmor oscillations from both isotopes are measured simultaneously. The ratio of the Larmor frequencies is used to calculate the ratio of effective atomic g-factors, g87 F/g85 F . We show that the atomic magnetometry experiment has a resolution of 0.68 parts per million (ppm) for measuring g87 F/g85 F . In order to understand systematic effects, we numerically model the atomic magnetometry signal using a system of differential equations. We present a comparison of the results of this model with an experimental survey of systematic effects. Numerical simulations and experimental surveys suggest that a more refined experiment is required to complete a precision measurement of atomic g-factors ratios that includes systematic effects.