Measurements of the hyperfine structure of $nP_J$ Rydberg states by microwave spectroscopy in Cs atoms

We present measurements of hyperfine structure (HFS) of the $nP_J$ Rydberg states for large principal quantum number $n$ range ($n=41-55$) employing the microwave spectroscopy in an ultra-cold cesium Rydberg ensemble. A microwave field with 30-$\mu$s duration couples the $ nS \to nP $ transition, yielding a narrow linewidth spectroscopy that approaches the Fourier limit, which allows us to resolve the hyperfine structure of $ nP_J $ states. By analyzing the hyperfine splittings of $nP_J$ states, we determine the magnetic-dipole HFS coupling constant $\bar{A}_{HFS,P_{1/2}}=3.760(26) ~$GHz for $P_{1/2}$ state, $\bar{A}_{HFS,P_{3/2}}= 0.718(27)~$GHz, and $ \bar{B}_{HFS,P_{3/2}}= -0.084(102)~$GHz for $P_{3/2}$ state, respectively. Systematic uncertainties caused by stray electromagnetic field, microwave field power and Rydberg interaction are analyzed. This measurement is significant for the investigation of Rydberg electrometry and quantum simulation with dipole interaction involving $nP_J$ state.