Cavity QED & Jaynes–Cummings Model
Single atom + single mode of light — Rabi oscillations and the quantum vacuum.
A two-level atom (ground $|g\rangle$, excited $|e\rangle$, frequency $\omega_a$) coupled to a single mode of a cavity (frequency $\omega_c$, annihilation $\hat a$) — the Jaynes–Cummings model:
$$\hat H = \frac{\hbar\omega_a}{2}\hat\sigma_z + \hbar\omega_c \hat a^\dagger \hat a + \hbar g(\hat\sigma_+ \hat a + \hat\sigma_- \hat a^\dagger).$$At resonance $\omega_c = \omega_a$, the dressed states $|n, \pm\rangle = (|e, n\rangle \pm |g, n+1\rangle)/\sqrt 2$ have energies separated by $2\hbar g \sqrt{n+1}$. Starting in $|e, 0\rangle$, the excitation oscillates between atom and cavity at the vacuum Rabi frequency $2g$:
$$P_{e}(t) = \cos^2(g t).$$Even with no photons present initially, the quantum vacuum drives the atom — a direct manifestation of vacuum fluctuations.
Experimentally realized in microwave (Rydberg atoms + superconducting cavities; Haroche 2012 Nobel) and optical (single atom + high-finesse mirrors; Kimble) regimes; in superconducting circuit QED (Wallraff, Schoelkopf) underlying modern transmon qubit hardware.