We report a combined experimental and theoretical study of non-conventional lasing from higher multi-exciton states of a few quantum dot-photonic crystal nanocavity. We show that the photon output is fed from saturable quantum emitters rather than a non-saturable background despite being rather insensitive to the spectral position of the mode. Although the exciton transitions of each quantum dot are detuned by up to $160$ cavity linewidths, we observe that strong excitation populates a multitude of closely spaced multi-exciton states, which partly overlap spectrally with the mode. The limited number of emitters is confirmed by a complete saturation of the mode intensity at strong pumping, providing sufficient gain to reach stimulated emission, whilst being accompanied by a distinct lasing threshold. Detailed second-order photon-correlation measurements unambiguously identify the transition to lasing for strong pumping and, most remarkably, reveal super-thermal photon bunching with $g^{(2)}(0)>2$ below lasing threshold. Based on our microscopic theory, a pump-rate dependent $beta$-factor $beta(P)$ is needed to describe the nanolaser and account for the interplay of multi-exciton transitions in the few-emitter gain medium. Moreover, we theoretically predict that the super-thermal bunching is related to dipole-anticorrelated multi-exciton recombination channels via sub- and super-radiant coupling below and above lasing threshold, respectively. Our results provide new insights into the microscopic light-matter-coupling of spatially separated emitters coupled to a common cavity mode and, thus, provides a complete understanding of stimulated emission in nanolasers with discrete emitters.
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