Jaynes-Cummings Model: Vacuum Rabi Oscillations

Two-level atom in a cavity — collapse and revival from photon number distribution

Parameters

Theory

H = ℏω_c a†a + ℏω_a σ_z/2 + ℏg(aσ₊ + a†σ₋)
Ω_n = √(n+1)·g (Rabi freq)
P_e(t) = Σ_n |c_n|² cos²(Ω_n t)
Collapse occurs at t_c ≈ 1/g (destructive interference of Ω_n). Revival at t_r ≈ 2π√n̄/g — constructive interference. Vacuum Rabi splitting: 2g. Fock state |e,n=0⟩ shows perfect Rabi oscillations at g·√1.

Live

t0
P_e
⟨n⟩
t_collapse
t_revival
Ω_vac