Continuous cavity QED with a hot atomic beam*

Superradiance is a phenomenon that can allow lasing directly from narrow clock transitions. Thanks to this property, steady-state superradiant lasers have been proposed as candidates to realize a new generation of frequency references: active optical clocks\footnote{J.B. Chen,  Chin. Sci. Bull. \textbf{54}, 348 (2009).}. We present an approach to achieve continuous superradiance using a hot atomic beam\footnote{L. Haonan \emph{et al.}, Phys. Rev. Lett. \textbf{125}, 253602 (2020).}. We reduce the size and complexity of a superradiant laser and explore the appearance of collective behaviour in a thermal beam apparatus. Resonance widths in hot gases of atoms are dominated by Doppler and transit time broadening. We reduce the first effect by the implementation of a slowing and velocity-selection scheme, so that the main requirement for superradiance is a collective linewidth broader than the transit time broadening. For both conditions we model the spectral properties of the transmission with a mean-field theory and find a good agreement with the experimental observations. This comparison shows the proximity to the superradiant phase transition. We demonstrate collective strong coupling on the semi-forbidden ${\rm ^1S_0\rightarrow ^3P_1}$ transition using a collimated atomic beam and an optical single-mode cavity. Interrogation with an external drive reveals normal mode splitting for ground-state atoms\footnote{ F. Famà\ \emph{et al.}, Phys. Rev. A \textbf{110}, 063721 (2024).} and up to 600\% optical amplification for an inverted atomic sample, suggesting proximity to self-sustained lasing.