| The optical properties of an ensemble of independent paramagnetic atoms depend on the nature,the degree,and the orientation of the ensemble’s spin polarization.The alkali metal atom magnetometer has a wide range of applications in the field of precision measurements due to its high sensitivity and easy miniaturization.This fact forms the basis for a variety of atomic sensors(gyroscopes and magnetometers)or metrological devices such as atomic clocks.The combination of resonant optical excitation and magnetic resonance has been an extremely valuable tool for atomic spectroscopy.The in-depth study of the alkali metal atomic magnetic resonance plays an important role in improving the sensitivity of atomic magnetometers and further expanding the application of atomic magnetometers.In this paper,we theoretically study the effect of high-order atomic multipole moments on the magnetic resonance of alkali metal atoms.In the model of optical-radio-frequency double resonance,the influence of atomic high-order multipole moments on the optical double resonance alignment magnetometer has been discussed.In addition,the physical mechanism of the light narrowing phenomenons occurring in two hyperfine ground states are investigated.Finally,the magneto-optical rotation effect is studied,and the physical mechanism of alignment to orientation conversion(AOC)is demonstrated.Consequently,the results mainly include the following three aspects:(1)We present a theoretical study of double-resonance alignment magnetometers using linearly polarized light,in which the effect of atomic high-order multipole moments is considered.Starting from the effective master equation of our system obtained by eliminating the excited state adiabatically,we derive the full evolution equations of the atomic multipole moments.The analytic solutions of resonance signals involving 4-order multipole moments effect are obtained by using perturbation approach.We present that the 4-order multipole moments effect is negligible in weak laser field,and the results reduce to that obtained by three-step approach.However,the role of 4-order multipole moments coupled by 2-order tensor moments is more significant with increasing Rabi frequency of light,and cannot be ignored.Meanwhile,the analytic expressions of relaxation processes are also studied,which is a linear combination of the laser-induced equivalent relaxation rate ΓL and the spin-exchange collision rate Γg.The expected domain of validity of the three-step approach on light power is roughly given by ΓL<1/2Γg.In addition,the steady-state results of resonance signals are presented in strong radio-frequency magnetic field,in that case,the physical mechanism of the splitting of resonance signals is discussed.These results are valid for arbitrary light power and for an arbitrarily oriented static magnetic field.(2)We present a theoretical study of the optical-radio-frequency(rf)double resonance on hyperfine ground states of alkali-metal atoms in the geophysical magnetic-field range,in which resonance circularly polarized laser light is used in the optical pumping and detection processes.The analytical expressions of the rf resonance signals corresponding to two ground states are obtained based on atomic multipole moments,where the alignment effect is considered and that is responsible for the resonance shape and linewidth especially when the optical power is relatively strong.In addition,we also obtain the analytical expressions of the linewidths of two separated resonance peaks and one presenting the competition process of the optical pumping,rf field and spin-exchange collision.Two different types of light narrowing phenomena are investigated by comparing the longitudinal relaxation rates of atomic multipole moments for two ground states.Applied to Rubidium and Cesium atoms,we show a particularly close agreement of our analytical results with more elaborate calculations using density-matrix theory.Our theoretical model is relevant for optimizing the sensitivity of magnetometers.(3)We theoretically investigate the magneto-optical rotation(MOR)effect in cesium atoms in the Voigt geometry,in which an off-resonance linearly-polarized laser beam serves as both pump and probe.By calculating the detailed evolution of atomic multipole moments truncated to second-rank,alignment-to-orientation conversion(AOC)effects are observed in two hyperfine ground states.The mechanisms responsible for this effect are demonstrated.The tensor ac-Stark shift produced by the optical pumping generates a nonlinear effect,resulting in atomic alignment directly coupled to orientation,which enables spin orientation to be obtained.Simultaneously,spin-exchange collisions lead to atomic alignment and orientation transfer between two ground-state manifolds.Additionally,we present the analytical expression of atomic spin polarization described by atomic multipole moments,and the contributions of the AOC effect to the optical-rotation signals are discussed in different light power regimes.Our results can be helpful for guiding MOR experiments by refining and optimizing the parameters. |
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