A single atom sits inside a high-finesse cavity that confines one mode of the field. The atom and the cavity photon exchange a quantum of energy at rate g; the cavity leaks photons at rate κ and the atom decays at rate γ. Their coupled linear response gives the steady-state transmission
T(δ) ∝ |κ / (κ/2 − iδ + g² / (γ/2 − iδ))|²
When g is small compared to κ and γ, the atom's excitation leaks away before it can be reabsorbed — the atom simply loads the cavity mode, giving one Lorentzian peak. Once g exceeds ≈|κ−γ|/4, the atom and cavity hybridize into two dressed states separated by Ω = 2√(g² − ((κ−γ)/4)²) — the vacuum Rabi doublet — visible even with no photons present beforehand, because it is a property of the coupled system itself.
- g — atom-cavity coupling strength; raise it to push the system from weak into strong coupling.
- κ — photon-loss rate of the cavity mirrors; higher κ washes the doublet back into a single broad peak.
- γ — the atom's own spontaneous-decay rate; also broadens and can hide the splitting.
- Trigger excitation — restarts the time-domain view with the atom excited and the cavity empty, so you can watch the coherent back-and-forth swap (or its rapid decay) play out.
Real-world relevance: this is the mechanism behind circuit-QED qubit readout and single-photon sources — engineers push g up (small mode volume, high-Q cavity) and κ, γ down (better mirrors, more isolated atoms) specifically to reach and exploit strong coupling.