Abstract
Quantum-optical research on semiconductor single-photon sources puts special emphasis on the measurement of the second-order correlation function g⁽²⁾(τ), arguing that g⁽²⁾(0)<1/2 implies the source field represents a good single-photon light source. We analyze the gain of information from g⁽²⁾(0) with respect to single photons. Any quantum state, for which the second-order correlation function falls below 1/2, has a nonzero projection on the single-photon Fock state. The amplitude p of this projection is arbitrary, independent of g⁽²⁾(0). However, one can extract a lower bound on the single-to-multi-photon-projection ratio. A vacuum contribution in the quantum state of light artificially increases the value of g⁽²⁾(0), cloaking actual single-photon projection. Thus, we propose an effective second-order correlation function g⁽²⁾(0), which takes the influence of vacuum into account and also yields lower and upper bounds on p. We consider the single-photon purity as a standard figure-of merit in experiments, reinterpret it within our results and provide an effective version of that physical quantity. Besides comparing different experimental and theoretical results, we also provide a possible measurement scheme for determining g⁽²⁾(0).