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Optomechanical wave mixing by a single quantum dot

Wave mixing is an archetypical phenomenon in bosonic systems. In optomechanics, the bidirectional conversion between electromagnetic waves or photons at optical frequencies and elastic waves or phonons at radio frequencies is building on precisely this fundamental principle. Surface acoustic waves (SAWs) provide a versatile interconnect on a chip and thus enable the optomechanical control of remote systems. Here we report on the coherent nonlinear three-wave mixing between the coherent fields of two radio frequency SAWs and optical laser photons via the dipole transition of a single quantum dot exciton. In the resolved sideband regime, we demonstrate fundamental acoustic analogues of sum and difference frequency generation between the two SAWs and employ phase matching to deterministically enhance or suppress individual sidebands. This transfer between the acoustic and optical domains is described by theory that fully takes into account direct and virtual multiphonon processes. Finally, we show that the precision of the wave mixing is limited by the frequency accuracy of modern radio frequency electronics.