Jaynes-Cummings: Cavity QED

A two-level atom coupled to a single cavity mode. For a Fock state, Rabi oscillations are perfectly periodic. For a coherent state, quantum interference causes collapse and revival — a purely quantum effect with no classical analogue.

<σ_z>(t) atom inversion
<n>(t) photon number

Field State

Atom-Cavity

Jaynes-Cummings Hamiltonian:
H = ℏωa†a + (ℏω₀/2)σ_z + ℏg(σ₊a + σ₋a†)

Fock state |n,↑⟩:
<σ_z>(t) = -cos(2g√(n+1)·t)
(periodic Rabi oscillations)

Coherent state |α⟩:
Sum over Fock states; different frequencies → collapse at t ≈ 1/g, revival at t_R ≈ 2π√n̄/g

Collapse-revival is a signature of photon number quantization — no classical field shows revivals.