Intrinsic process for upconversion photoluminescence via $K$-momentum phonon coupling in carbon nanotubes

We investigate the intrinsic microscopic mechanism of photon upconversion in air-suspended single-walled carbon nanotubes through photoluminescence and upconversion photoluminescence spectroscopy. Nearly linear excitation power dependence of upconversion photoluminescence intensity is observed, indicating a one-photon process as the underlying mechanism. In addition, we find a strongly anisotropic response to the excitation polarization which reflects the intrinsic nature of the upconversion process. In upconversion photoluminescence excitation spectra, three peaks are observed which are similar to photoluminescence sidebands of the $K$-momentum dark singlet exciton. The features in the upconversion photoluminescence excitation spectra are well reproduced by our second-order exciton-phonon interaction model, enabling the determination of phonon energies and relative amplitudes. The analysis reveals that the upconversion photoluminescence can be described as a reverse process of the sideband emission linked to the $K$-momentum phonon modes. The validity of our model is further reinforced by temperature-dependent upconversion photoluminescence excitation measurements reflecting variations in the phonon population. Our findings underscore the pivotal role of the resonant exciton-phonon coupling in pristine carbon nanotubes and presents potential for advanced optothermal technologies by engineering the excitation pathways.