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Alkali-metal-vapor magnetometers, using coherent precession of polarizedatomic spins for magnetic field measurement, have become one of the mostsensitive magnetic field detectors. Their application areas range frompractical uses such as detections of NMR signals to fundamental physicsresearch such as searches for permanent electric dipole moments. One of themain noise sources of atomic magnetometers comes from the light shift thatdepends on the frequency of the pump laser. In this work, we theoreticallystudy the light shift, taking into account the relaxation due to the opticalpumping and the collision between alkali atoms and between alkali atoms and thebuffer gas. Starting from a full master equation containing both the ground andexcited states, we adiabatically eliminate the excited states and obtain aneffective master equation in the ground-state subspace that shows an intuitivepicture and dramatically accelerates the numerical simulation. Solving thiseffective master equation, we find that in the light-narrowing regime, wherethe line width is reduced while the coherent precession signal is enhanced, thefrequency-dependence of the light shift is largely reduced, which agrees withexperimental observations in cesium magnetometers. Since this effective masterequation is general and is easily solved, it can be applied to an extensiveparameter regime, and also to study other physical problems inalkali-metal-vapor magnetometers, such as heading errors.

Reduction of frequency-dependent light shifts in light-narrowing regimes: A study using effective master equations