  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.
