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The optimal detuning of the pump light at the rubidium D2 line is calculated and experimentally validated. A three-level optically end-pumped model in a hot rubidium vapor cell is demonstrated, which takes into account the hyperfine structure of the ground state, various collisional processes, and the nonlinear absorption of the pump light along the cell length. By developing a constrained optimization model, we calculate the optimal detuning of the pump light that maximizes the average excited state atom concentration in the cell. Experimentally, a 1529 nm probe light at higher levels, which is attenuated to the weak-probe limit, is introduced to accurately characterize the excited state atom concentration. Coupling with the experimental results, the variation of the pump light optimal detuning with the temperature and the pump light intensity at the unsaturated pumping is analyzed. At the optimal detuning point, the theoretical decay function of the pump light percentage along the vapor cell length almost coincides regardless of the temperature and the pump light intensity changes. Moreover, the theoretical fitted pump light decay function at optimal detuning is predicted. The fitted pump light percentage exiting the vapor cell is 4.75%. A fast implementation method to achieve the maximal average excited state atom concentration in the experiment is demonstrated.

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