The optical resonance linewidth of a single quantum emitter provides a direct measurement of decoherence in the system, which is a quantity of interest to certain quantum technological applications and ultimately sets a fundamental limitation for these materials. However, accessing the homogeneous linewidth has proven problematic in semiconductor nanocrystals (NCs) due to the effect of spectral diffusion (SD), which is a random fluctuation of the transition energy. Instabilities in the spectral position are discouraging for potential applications in for example coherent control of quantum states and coupled systems, thus so far there have been few reports using NCs in such applications. At cryogenic temperatures high quality NCs exhibit slow relaxation between closely spaced band-edge states resulting in stable multiline spectra. Inter-state relaxation properties are explored using a near-resonant photoluminescence excitation of higher-lying states to selectively excite specific band-edge states, revealing significant population redistribution, indicative of slow relaxation between the band-edge states. This state-selective excitation reveals unexpected spin-dependent non-radiative relaxation channels that need to be taken into account in order to understand the final state populations. In colloidal NCs, thermal excitation of acoustic phonons can be inhibited at cryogenic temperatures, eliminating a major dephasing mechanism, therefore one might expect to observe lifetime limited transitions in high quality colloidal NCs. High-resolution excitation scans of individual spectral lines of apparently ultra-stable NCs, reveal spectral lines significantly broader than the lifetime limit. By performing a series of successive scans over the same spectral line, the underlying SD is revealed. This SD is notable in that it results in symmetric broadening of the excitation scan, indicating that the origin is not photo-induced. Thus a persistent contribution to SD is revealed. The magnitudes of the spectral shifts are consistent with environmental charge noise known to be associated with random polymer matrices and so most likely emanate from the disordered local environment of the NC, which may include the ligand shell. This persistent SD ultimately limits the linewidth of the band-edge states in colloidal NCs to the 1 GHz regime, approximately an order of magnitude greater than the lifetime limit.< Réduire