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Physical Review A

Theoretical study of the alignment-to-orientation conversion in magneto-optical rotation based on atomic multipole moments

Pan-li Qi, Xu‐xing Geng, Guoqing Yang, Shao‐ping Wu, Guangming Huang, Gao‐xiang Li

Published Mar 29, 2022• 2 citations
Publisher

Abstract

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.

DOI
10.1103/physreva.105.033112

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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.
Abstract In this study we explored the possibilities for observing the angular momentum alignment-to-orientation conversion (AOC) in the ground state of various alkali metals: K, Rb, Cs. For theoretical analysis we used a model that is based on the Optical Bloch equations for the density matrix. In our model we took into account the interaction of the laser light with all hyperfine levels, which are mixed as the magnetic field increases. The radiation’s coherence properties were also included. Finally, the results were averaged over the Doppler profile. Additionally we simulated signals where the ground- or the excited-state coherent processes were numerically switched off in order to determine the origins of the features of the obtained signals. We also performed experiments on Cs atoms with two laser beams: a linearly polarized Cs D 1 pump and circularly polarized Cs D 2 probe. We used the pump beam to create angular momentum alignment in the ground state and observed the transmission signal of the probe beam as we changed the magnetic field. A detailed analysis of the experimentally obtained transmission signal from a single circularly polarized probe laser component is provided. Finally, prospects for observing AOC experimentally are discussed, as well as experiments were even a weak AOC signal could lead to systematic errors.
We evaluated the alignment-to-orientation conversion (AOC) at the cesium D1 line to improve a nonlinear magneto–optical rotation (NMOR) optical atomic magnetometer’s signal amplitude and bandwidth. For the 6 2S1/2 F = 3 → 6 2P1/2 F′ = 4 transition, the AOC-related NMOR achieves a 1.7-fold enhancement in signal amplitude compared to the conventional NMOR, benefiting from narrow linewidth and ultraweak power broadening. Therefore, an effective amplitude-to-linewidth ratio is maintained in the high-laser-power region. This method is beneficial for detecting high-frequency magnetic signals in nuclear magnetic resonance and biomagnetism, as the NMOR magnetometer bandwidth increases with laser power.
In this study we explored the angular momentum alignment-to-orientation conversion occurring in various alkali metals -- K, Rb, Cs. We used a theoretical model that is based on Optical Bloch equations and uses the density matrix formalism. Our model includes the interaction of all neighboring hyperfine levels, the mixing of magnetic sublevels in an external magnetic field, the coherence properties of the exciting laser radiation, and the Doppler effect. Additionally we simulated signals where the ground- or the excited-state coherent processes were switched off allowing us to determine the origins of obtained signals. We also performed experiments on Cs atoms with two laser beams: linearly polarised Cs D1 pump and circularly polarized Cs D2 probe. We used the pump beam to create angular momentum alignment in the ground state and observed the transmission signal of the probe beam as we changed the magnetic field. Full analysis of the experimentally obtained transmission signal from a single circularly polarized probe laser component is provided.
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 the four-order multipole moments effect are obtained by using the perturbation approach. We present that the four-order multipole moments effect is negligible in the weak laser field, and the results reduce to that obtained by a three-step approach. However, the role of four-order multipole moments coupled by two-order tensor moments is more significant with the increasing Rabi frequency of light, which cannot be ignored. Meanwhile, the analytic expressions of relaxation processes are also studied, which are a linear combination of the laser-induced equivalent relaxation rate Γ L and the spin-exchange collision rate Γ g . The expected domain of validity of the three-step approach on light power is roughly given by Γ L < 1 2 Γ g . In addition, the steady-state results of resonance signals are presented in a 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.
The mutual coupling between the polarization moments with ranks of different parity is theoretically considered. The manifestation of this mutual coupling has been revealed previously in experiments on magnetic resonance of optically oriented cesium atoms. The two well-known types of the coupling between the polarization moments are considered: the field coupling of these moments that occur due to the breaking of the hyperfine coupling between the electronic and nuclear moments of the alkali atom by the magnetic field and the light coupling of the moments due to the absorption of the pumping light by polarized atoms. The experimentally observed similarity in the shape of resonance signals of alignment and orientation upon circularly polarized pumping can be explained by the fact that, for alkali atoms, the generation of alignment by light at the wavelength of the D 1 line is of low efficiency. Therefore, alignment arises mainly from orientation by means of either the field or the light coupling of polarization moments. For metastable 23 S 1 4He atoms, no influence of the orientation on the alignment was observed because, in these atoms, the field coupling between the polarization moments is absent and the light coupling is not displayed because the generation of alignment by the circularly polarized pumping light is more efficient than the creation of alignment from orientation by means of light coupling of polarization moments.
The creation and detection of atomic polarization is examined theoretically through the study of basic optical-pumping mechanisms and absorption and fluorescence measurements and the dependence of these processes on the size of ground- and excited-state hyperfine splittings is determined. The consequences of this dependence are studied in more detail for the case of nonlinear magneto-optical rotation in the Faraday geometry (an effect requiring the creation and detection of rank-two polarization in the ground state) with alkali-metal atoms. Analytic formulas for the optical rotation signal under various experimental conditions are presented.