Quantum kinetics of squeezed lattice displacement generated by phonon down conversion

Abstract

We study the fluctuation properties of longitudinal acoustic (LA) phonons generated by the anharmonic decay of coherent longitudinal optical phonons in a bulk semiconductor and a quantum dot. This process is comparable to the down conversion of photons, which is well known to generate squeezed photons. We use a quantum kinetic model to calculate the fluctuations of lattice displacement and momentum. This allows us to analyze the strength and the spatial distribution of the fluctuations. It is shown that the fluctuations may fall below their vacuum value, i.e., squeezing occurs. The squeezing only persists for short times due to fast dephasing of the different LA phonon modes and the increasing LA phonon population. In the quantum dot case, it is found that although LA phonon wave packets travel out of the quantum dot, the squeezing does not leave the vicinity of the dot but remains confined.