The absence of strong losses in high-beta nanolasers makes the identification of the onset of lasing difficult to pinpoint, as the input-output characteristics can become almost thresholdless. The second-order photon correlation function g2(0) has become a valuable tool to assess the coherence properties of nanolasers, as its transition to a value of 1 clearly marks the laser threshold. Most measurements of the zero-delay-time autocorrelation function involve temporal averaging over g2(tau) due to the finite time resolution of the photon detectors. In the past, a generalized Siegert relation has been used to approximately obtain g2(tau). Using full quantum-optical two-time calculations, we address the question in how far it can be used in the partially coherent regime of conventional nanolasers that show a soft transition to lasing, and in few-emitter nanolasers that operate close to or in the regime of strong light-matter coupling.
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