Optical gain in colloidal quantum dots is limited by biexciton absorption, not biexciton recombination

Despite three decades of experimental study, optical gain in colloidal quantum dots still lacks a microscopic theory capable of explaining gain thresholds approaching one exciton per dot, their size dependence, or the anomalously small effective stimulated-emission cross sections observed across materials. Existing descriptions treat quantum dots as effective two-level systems comprised of an exciton and a biexciton, attributing gain thresholds to biexciton Auger recombination. This assumption is inconsistent with state-resolved optical pumping experiments and basic spectroscopic constraints. Here we present a microscopic theory of optical gain explicitly anchored in the Einstein relations governing absorption and stimulated emission. Within this framework, gain is determined by a spectral balance between stimulated emission from single excitons and excited-state absorption into biexcitonic manifolds, rather than by biexciton lifetimes. Using a spin-boson description of excitons coupled to a lattice bath, we show that gain thresholds and effective gain cross sections are controlled by the interplay of biexciton stabilization and exciton-lattice dressing. The theory unifies disparate materials by quantitatively explaining all longstanding gain phenomenology in CdSe quantum dots and predicts a continuous crossover to effective four-level, near-thresholdless gain in dynamically disordered lattices such as perovskite quantum dots.