  We study theoretically the fluctuation properties of acoustic phonons created
in a semiconductor quantum dot after ultrafast optical excitation. An
excitation with a single ultrafast pulse creates an exciton confined to the
quantum dot, which is coupled to longitudinal acoustic phonons. This leads to
the formation of a polaron in the quantum dot accompanied by the emission of a
phonon wave packet. We show that the fluctuations of the lattice displacement
associated with the wave packet after a single laser pulse excitation in
resonance with the exciton transition are always larger than their respective
vacuum values. Manipulating the exciton with a second pulse can result in a
reduction of the fluctuations below their vacuum limit, which means that the
phonons are squeezed. We show that the squeezing properties of the wave packet
strongly depend on the relative phase and the time delay between the two laser
pulses.
