Third-order photon correlations to extract single nanocrystal multiexciton properties in solution

Colloidal semiconductor nanocrystals are considered promising materials for high-flux optical 
applications including lasing, light-emitting diodes, biological imaging, and quantum optics. In 
high-flux applications, multiexcitons can significantly contribute to emission, influencing its 
brightness, spectral purity, and kinetics. As a result, understanding and controlling multiexciton 
emission in colloidal nanocrystal materials is of the utmost importance. In the past, single
nanocrystal photon correlation methods have been applied to understand biexciton and 
triexciton efficiencies, lifetimes, and spectra. While powerful, such methods suffer from user 
selection bias and require stable emission from single nanocrystals. To compensate for this 
shortcoming, second-order correlation methods were developed to extract sample-averaged 
biexciton properties from a solution of nanocrystals. Until now, however, the analogous third
order solution photon correlation methods remained unexplored. In this work, we present a pair 
of third-order photon correlation techniques to obtain the sample-averaged single nanocrystal 
triexciton quantum yield and lifetime in a solution-phase experiment. These techniques derive 
from the relationship between the Poisson probability of nanocrystal photon absorption and the 
intrinsic probability of nanocrystal photon emission. We validate the theoretical background of 
these techniques by creating a numerical model to simulate the diffusion and emission of many 
nanocrystals in solution. Our simulations confirm that the average triexciton quantum yield and 
triexciton lifetime can be extracted from a solution of nanocrystals. These techniques will 
enable researchers to gain a better understanding of the fundamental multiexciton properties of 
colloidal nanocrystals.