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The paradigm of cavity QED is a two-level emitter interacting with a highquality factor single mode optical resonator. The hybridization of the emitterand photon wave functions mandates large vacuum Rabi frequencies and longcoherence times; features that so far have been successfully realized withtrapped cold atoms and ions and localized solid state quantum emitters such assuperconducting circuits, quantum dots, and color centers. Thermal atoms on theother hand, provide us with a dense emitter ensemble and in comparison to thecold systems are more compatible with integration, hence enabling large-scalequantum systems. However, their thermal motion and large transit timebroadening is a major challenge that has to be circumvented. A promising remedycould benefit from the highly controllable and tunable electromagnetic fieldsof a nano-photonic cavity with strong local electric-field enhancements.Utilizing this feature, here we calculate the interaction between fast moving,thermal atoms and a nano-beam photonic crystal cavity (PCC) with large qualityfactor and small mode volume. Through fully quantum mechanical calculations,including Casimir-Polder potential (i.e. the effect of the surface on radiationproperties of an atom) we show, when designed properly, the achievable couplingbetween the flying atom and the cavity photon would be strong enough to lead toRabi flopping in spite of short interaction times. In addition, thetime-resolved detection of different trajectories can be used to identifysingle and multiple atom counts. This probabilistic approach will findapplications in cavity QED studies in dense atomic media and paves the waytowards realizing coherent quantum control schemes in large-scale macroscopicsystems aimed at out of the lab quantum devices.

Cavity QED Based on Thermal Atoms Interacting with a Photonic Crystal Cavity: A Feasibility Study