\textbf{Stimulated emission and lasing from all-inorganic perovskite quantum dots}

We present superior optical gain and lasing properties in a new class of emerging quantum materials, the colloidal all-inorganic cesium lead halide perovskite quantum dots (IPQDs) (CsPbX$_{\mathrm{3}}$, X $=$ Cl, Br, I). Our result has indicated that such material system show combined merits of both colloidal quantum dots and halide perovskites. Low-threshold and ultrastable stimulated emission was demonstrated under atmospheric condition. The flexibility and advantageous optical gain properties of these CsPbX$_{\mathrm{3\thinspace }}$IPQDs were manifested by demonstration of an optically pumped micro-laser. The nonlinear optical properties including the multi-photon absorption and resultant photoluminescence of the CsPbX$_{\mathrm{3}}$ nanocrystals were investigated. A large two-photon absorption cross-section of up to \textasciitilde 1.2\texttimes 105 GM is determined from 9 nm-sized CsPbBr$_{\mathrm{3}}$ nanocrystals. Moreover, low-threshold frequency-upconverted stimulated emission by two-photon absorption was observed from the thin films of close-packed CsPbBr$_{\mathrm{3}}$ nanocrystals. We further realize the three-photon pumped stimulated emission in green spectra range from colloidal IPQD.