Jaynes-Cummings model: a two-level atom (qubit) coupled to a single cavity mode. Exactly solvable — the Hamiltonian in the rotating wave approximation is:
H = ħω(a†a + σ†σ) + ħg(a†σ + aσ†) + ħΔσ†σ
Vacuum Rabi splitting 2g appears in the transmission spectrum. With a
coherent state |α⟩, the atom undergoes Rabi oscillations at multiple frequencies g√(n+1), leading to
collapses and quantum revivals at T_rev = 2π⟨n̄⟩/g. The left panel shows the cavity with photon field; right shows the dressed-state spectrum (avoided crossing vs detuning).