Exciton lasing in carbon nanotubes below the population inversion threshold via phonon-mediated stimulated emission

Excitonic optical transitions in carbon nanotubes (CNTs) have been extensively studied for at least two decades. However, exploiting these transitions to produce a lasing effect has been proved unpractical due to the difficulties of achieving an excitonic population inversion in carbon nanotubes. In this work we show that lasing is theoretically possible at a much lower exciton population threshold by taking advantage of phonon stimulated emission. Specifically, the so-called Anti-Stokes transitions, where light is generated by the creation of a phonon and the annihilation of an exciton, can be used to sustain the coherent emission of photons. These transitions have been overlooked for long due to their low intensity as a consequence of the low occupancy of the associated phonon branches. We show that the best conditions to achieve the lasing effect are met in CNTs with i) excitons of non-zero momentum, ii) a strong exciton-phonon coupling and iii) narrow exciton transitions.