  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.
