Atomic magnetic resonance induced by amplitude-, frequency-, or polarization-modulated light

In recent years diode laser sources have become widespread and reliable tools in magneto-optical spectroscopy. In particular, laser-driven atomic magnetometers have found a wide range of practical applications. More recently, so-called magnetically silent variants of atomic magnetometers have been developed. While in conventional magnetometers the magnetic resonance transitions between atomic sublevels are phase-coherently driven by a weak oscillating magnetic field, silent magnetometers use schemes in which either the frequency (FM) or the amplitude (AM) of the light beam is modulated. Here we present a theoretical model that yields algebraic expressions for the parameters of the multiple resonances that occur when either amplitude-, frequency- or polarization-modulated light of circular polarization is used to drive the magnetic resonance transition in a transverse magnetic field. The relative magnitudes of the resonances that are observed in the transmitted light intensity at harmonic m of the Larmor frequency \omega_L (either by DC or phase sensitive detection at harmonics q of the modulation frequency \omega_mod) of the transmitted light are expressed in terms of the Fourier coefficients of the modulation function. Our approach is based on an atomic multipole moment representation that is valid for spin-oriented atomic states with arbitrary angular momentum F in the low light power limit. We find excellent quantitative agreement with an experimental case study using (square-wave) amplitude-modulated (AM) light.