  We theoretically propose optical phonon lasing in a double quantum dot (DQD)
fabricated on a semiconductor substrate. No additional cavity or resonator is
required. An electron in the DQD is found to be coupled to only two
longitudinal optical phonon modes that act as a natural cavity. When the energy
level spacing in the DQD is tuned to the phonon energy, the electron transfer
is accompanied by the emission of the phonon modes. The resulting
non-equilibrium motion of electrons and phonons is analyzed by the rate
equation approach based on the Born-Markov-Secular approximation. We show that
the lasing occurs for pumping the DQD via electron tunneling at rate much
larger than the phonon decay rate, whereas a phonon antibunching is observed in
the opposite regime of slow tunneling. Both effects disappear by an effective
thermalization induced by the Franck-Condon effect in a DQD fabricated in a
suspended carbon nanotube with strong electron-phonon coupling.
