Spontanemission

Spontanemission, or spontaneous emission, is the process by which an excited atomic, ionic, or molecular state decays to a lower energy state by emitting a photon in the absence of external stimulation. In quantum electrodynamics this irreversible decay arises from the interaction of the system with the quantized electromagnetic vacuum; fluctuations of the vacuum drive transitions between energy levels.

Each possible decay j → i has a probability per unit time Aji, called the Einstein A coefficient. The total decay rate from level j is Aj = sum over i of Aji, and the lifetime τj is 1/Aj. The emitted photon carries energy ΔE = Ej − Ei, so its frequency is ν = ΔE/h. The spectral line is naturally broadened by the finite lifetime, yielding a Lorentzian with full width at half maximum Γ ≈ Aj. Selection rules and the dipole moment determine which transitions are allowed and thus the magnitude of Aji.

Spontaneous emission differs from stimulated emission, where photon occupancy of the mode influences the transition rate. Einstein's A and B coefficients relate spontaneous and stimulated processes. In practical terms, spontaneous emission sets the fundamental limits of fluorescence lifetimes and radiative linewidths, and is modified in cavities (Purcell effect) or structured environments.

Historically, Einstein proposed the A and B coefficients in 1917, and the quantum-field description of spontaneous emission was developed in the mid-20th century. Applications include fluorescence spectroscopy, lighting, LEDs, and lasers, where stimulated emission is harnessed for gain while spontaneous emission provides the initial photons and radiative decay channels.