Optical phonon lasing and its detection in transport through semiconduc- tor double quantum dots

We theoretically propose optical phonon lasing for a double quantum dot (DQD) fabricated in a semiconductor substrate. No additional cavity or resonator is required. We show that the DQD couples to only two phonon modes that act as a natural cavity. The pumping to the upper level is realized by an electric current through the DQD under a finite bias. Using the rate equation in the Born-Markov-Secular approximation, we analyze the enhanced phonon emission when the level spacing in the DQD is tuned to the phonon energy. We find the phonon lasing when the pumping rate is much larger than the phonon decay rate, whereas anti-bunching of phonon emission is observed when the pumping rate is smaller.\footnote{R. Okuyama {\it et al.}, J.\ Phys.\ Soc.\ Jpn.\ {\bf 82}, 013704 (2013); New J.\ Phys.\ {\bf 15}, 083032 (2013).} Our theory can be also applicable to DQDs embedded in nanomechanical resonators to control the vibrating modes. We discuss detection of amplified modes using the electric current and its noise through the DQD, and another DQD fabricated nearby.