Defect-decorated
single-wall carbon nanotubes have shown rapid
growing potential for imaging, sensing, and the development of room-temperature
single-photon sources. The key to the highly nonclassical emission
statistics is the discrete energy spectrum of defect-localized excitons.
However, variations in defect configurations give rise to distinct
spectral bands that may compromise single-photon efficiency and purity
in practical devices, and experimentally it has been challenging to
study the exciton population distribution among the various defect-specific
states. Here, we performed photon correlation spectroscopy on hexyl-decorated
single-wall carbon nanotubes to unravel the dynamics and competition
between neutral and charged exciton populations. With autocorrelation
measurements at the single-tube level, we prove the nonclassical photon
emission statistics of defect-specific exciton and trion photoluminescence
and identify their mutual exclusiveness in photoemissive events with
cross-correlation spectroscopy. Moreover, our study reveals the presence
of a dark state with population-shelving time scales between 10 and
100 ns. These new insights will guide further development of chemically
tailored carbon nanotube states for quantum photonics applications.