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We develop a theoretical frame to investigate the spectral dependence of the brightness of a single-photon source made of a solid-state nanoemitter embedded in a high-quality factor microcavity. This study encompasses the cases of localized excitons embedded in a one-, two-, or three-dimensional matrix. The population evolution is calculated based on a spin-boson model, using the noninteracting blip approximation. We find that the spectral dependence of the single-photon source brightness (hereafter called spectral efficiency) can be expressed analytically through the free-space emission and absorption spectra of the emitter, the vacuum Rabi splitting, and the loss rates of the system. In other words, the free-space spectrum of the emitter encodes all the relevant information on the interaction between the exciton and the phonon bath to obtain the dynamics of the cavity-coupled system. We compute numerically the spectral efficiency for several types of localized emitters differing by the phonon bath dimensionality. In particular, in low-dimensional systems where this interaction is enhanced, a pronounced asymmetric energy exchange between the emitter and the cavity on the phonon sidebands yields a considerable extension of the tuning range of the source through phonon-assisted cavity feeding, possibly surpassing that of a purely resonant system.

We report on the nonlinear optical response of a monochiral sample of (6,5) single-wall carbon nanotubes by means of broadband two-color pump-probe spectroscopy with selective excitation of the ${S}_{11}$ excitons. By using a moment analysis of the transient spectra, we show that all the nonlinear features can be accurately accounted for by elementary deformations of the linear absorption spectrum. The photogeneration of ${S}_{11}$ excitons induces a broadening and a blueshift of both the ${S}_{11}$ and ${S}_{22}$ excitonic transitions. In contrast, only the ${S}_{11}$ transition shows a reduction of oscillator strength, ruling out population up-conversion. These nonlinear signatures result from many-body effects, including phase-space filling, wave-function renormalization, and exciton collisions. This framework is sufficient to interpret the magnitude of the observed nonlinearities and stress the importance of intersubband exciton interactions. Remarkably, we show that these intersubband interactions have the same magnitude as the intraband ones and bring the major contribution to the photobleaching of the ${S}_{22}$ excitonic transition upon ${S}_{11}$ excitation through energy shift and broadening.

The emission linewidth is a key figure of merit for a quantum emitter. This paper reports on the possibility of reducing the spectral linewidth of single-wall carbon nanotubes. It demonstrates an order of magnitude narrower linewidths compared to the available data due to the enhanced crystalline quality of the carbon nanotubes synthesized by using a laser ablation technique.