  We report on high-resolution microwave spectroscopy of cesium Rydberg
$(n+2)D_{5/2}\rightarrow nF_{J}$ transitions in a cold atomic gas. Atoms
laser-cooled and trapped in a magnetic-optical trap are prepared in the $D$
Rydberg state using a two-photon laser excitation scheme. A microwave field
transmitted into the chamber with a microwave horn drives the Rydberg
transitions, which are probed via state selective field ionization. Varying
duration and power of the microwave pulse, we observe Fourier side-band spectra
as well as damped, on-resonant Rabi oscillations with pulse areas up to
$\gtrsim 3 \pi$. Furthermore, we investigate the Zeeman effect of the clearly
resolved $nF_J$ fine-structure levels in fields up to 120~mG, where the
transition into $nF_{7/2}$ displays a thee-peak Zeeman pattern, while
$nF_{5/2}$ shows a two-peak pattern. Our theoretical models explain all
observed spectral characteristics, showing good agreement with the experiment.
Our measurements provide a pathway for the study of high-angular-momentum
Rydberg states, initialization and coherent manipulation of such states,
Rydberg-atom macrodimers, and other Rydberg-atom interactions. Furthermore, the
presented methods are suitable for calibration of microwave radiation as well
as for nulling and calibration of DC magnetic fields in experimental chambers
for cold atoms.
