Figure 10.

(a) Optical transitions in a neutral (left), singly charged (middle), and doubly charged (right) QD. Black and red arrows show optical transitions that correspond to, respectively, absorption and stimulated emission. P₀, P_X, P_XX are the probabilities for the QD to be in the ground state (|0⟩), single-exciton state (|X⟩), or biexciton (|XX⟩) state. γ is the rate of a single spin-allowed transition. In the neutral QDs, single excitons do not contribute to optical gain. In this case, optical gain is the net result of the competition between stimulated emission from the biexcitons and absorption due to the unexcited QDs. In the singly charged QDs, net gain is due to the competition between stimulated emission from the charged excitons (trions) and absorption arising from the unexcited QDs. In the doubly charged QDs, ground-state absorption is eliminated, and gain is due to stimulated emission from the doubly charged excitons. (b) A schematic depiction of the optical gain-threshold condition (or the condition for “optical transparency”) in a neutral (XX, left), singly charged (X^–, center) and doubly charged (X^2–, right) QD. Panels (a, b) adapted with permission from ref (61). Copyright 2019, The American Association for the Advancement of Science.