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We theoretically and experimentally investigate the Rydbergelectromagnetically induced transparency (EIT) and Autler-Townes (AT) splittingof $^{87}$Rb vapor under the combined influence of a magnetic field and amicrowave field. In the presence of static magnetic field, the effect of themicrowave field leads to the dressing and splitting of each $m_F$ state,resulting in multiple spectral peaks in the EIT-AT spectrum. A simplifiedanalytical formula was developed to explain the EIT-AT spectrum in a staticmagnetic field, and the calculations are in excellent agreement withexperimental results.We further studied the enhancement of the Rydberg atommicrowave electric field sensor performance by making use of the splittinginterval between the two maximum absolute $m_F$ states under static magneticfield. The traceable measurement limit of weak electric field by EIT-ATsplitting method was extended by an order of magnitude, which is promising forprecise microwave electric field measurement.

Magnetic-field-induced splitting of Rydberg Electromagnetically Induced Transparency (EIT) and Autler-Townes (AT) spectra in $^{87}$Rb vapor cell