We compare the Faraday spectrum with the dispersion spectrum near the
D2 line of Rb atoms immersed in a high density Xe buffer gas. We observe deviations from the standard Becquerel relation, which relates the Faraday effect of an atomic gas to its dispersion. The deviations are due to coupling of the Rb valence electron to the Xe environment. The Rb
D2 transition dipole moment becomes rotationally locked to the instantaneous collision axes at Xe densities of \ensuremath{\sim}
1020 ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}3}$.
We investigate, theoretically and experimentally, the onset of modified electronic precession due to quasimolecular behavior in dense atomic gases. The close connection between the angular coupling of collision pairs and a modification of the Faraday effect is pointed out. We have observed the onset of this quasimolecular modification of the atomic Faraday effect with high-resolution laser measurements of the absorption and Faraday spectra near the
D2 line of Rb atoms immersed in high-density buffer gases. The atomic Faraday effect itself is also affected by the presence of nuclear spin; this modifies the electronic precession through angular-momentum coupling. We describe how to separate the effect of nuclear spin from the effects due to quasimolecular behavior. In this way we establish the existence of angular coupling of the Rb valence electrons to neighboring buffer-gas atoms at densities above \ensuremath{\sim}2\ifmmode\times\else\texttimes\fi{}
1019 ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}3}$ in Xe buffer gas. In He buffer gas, quasimolecular modifications of the Faraday effect are approximately two times smaller than for Xe.
The linear Faraday effect is used to implement a continuous measurement of the spin of a sample of laser-cooled atoms trapped in an optical lattice. One of the optical lattice beams serves also as a probe beam, thereby allowing one to monitor the atomic dynamics in real time and with minimal perturbation. A simple theory is developed to predict the measurement sensitivity and associated cost in terms of decoherence caused by the scattering of probe photons. Calculated signal-to-noise ratios in measurements of Larmor precession are found to agree with experimental data for a wide range of lattice intensity and detuning. Finally, quantum back-action is estimated by comparing the measurement sensitivity to spin projection noise, and shown to be insignificant in the current experiment. A continuous quantum measurement based on Faraday spectroscopy in optical lattices may open up new possibilities for the study of quantum feedback and classically chaotic quantum systems.