Einstein coefficients

Einstein coefficients quantify transition rates between atomic energy levels: absorption and stimulated emission depend on radiation intensity, while spontaneous emission does not.

Absorption: A process in which an atom gains energy by taking up a photon and moving to a higher energy state. The coefficient B₁₂ gives the probability of this transition per unit radiation intensity.
Atomic energy level: A discrete allowed energy state of an atom. Each coefficient is defined for transitions between a specified pair of atomic levels.
Laser: A device that produces coherent light through stimulated emission and optical feedback. Laser gain depends on stimulated emission overcoming absorption in a chosen transition.
Albert Einstein: A theoretical physicist whose work reshaped modern physics, including relativity and quantum theory. In 1916–1917, he introduced the coefficients while analyzing radiation in thermal equilibrium.
Oscillator strength: A dimensionless measure of the strength of an atomic or molecular transition relative to a classical oscillator. It summarizes transition strength rather than separately specifying absorption, stimulated emission, and spontaneous emission rates.
Stimulated emission: A process in which an incoming photon prompts an excited atom to emit a second photon matching it in frequency, direction, and phase. The coefficient B₂₁ measures this radiation-driven transition.
Photon: A quantum of electromagnetic radiation carrying energy proportional to its frequency. Absorption and emission change an atom's state by exchanging photons.
Population inversion: A condition in which an upper energy level is more populated than a lower level, accounting for degeneracy. It lets stimulated emission exceed absorption and enables optical gain.
On the Quantum Theory of Radiation: Einstein's 1917 paper developing a quantum account of radiation emission and absorption. It presents the argument that establishes relations among the three transition coefficients.
Fermi's golden rule: A quantum-mechanical formula for transition rates caused by a weak perturbation into a continuum of final states. It derives rates from interaction matrix elements, whereas Einstein coefficients parameterize radiative transitions.

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