Multiphoton dressed Rydberg excitations in a microwave cavity with ultracold Rb atoms

We investigate magneto-optical trap loss spectroscopy of Rydberg excited ${}^{85}$Rb ($66\le n\le 68S_{1\mathrm{/}2}$) atoms, placed inside a tailored microwave cavity. The cavity frequency at 13.053 GHz is in resonance with the $67S_{1\mathrm{/}2}\to 66P_{3\mathrm{/}2}$ transition, inducing a ladder multiphoton microwave Rydberg absorption and emission. The observed spectra are modeled with an extended Jaynes-Cumming formalism that accounts for multiphoton absorption from and emission into the cavity, the loss from the trap due to Rydberg excitation, and cavity imperfection. We calculate the average photons in each spectral feature and find evidence for fractional photon emission into the cavity modes. The microwave cavity Rydberg spectroscopy in this work should inform the application and technology development of Rydberg based sensors and hybrid Rydberg atom-superconducting resonator quantum gates.