  The study of the fundamental properties of phonons is crucial to understand
their role in applica- tions in quantum information science, where the active
use of phonons is currently highly debated. A genuine quantum phenomenon
associated with the fluctuation properties of phonons is squeezing, which is
achieved when the fluctuations of a certain variable drop below their
respective vacuum value. We consider a semiconductor quantum dot in which the
exciton is coupled to phonons. We review the fluctuation properties of the
phonons, which are generated by optical manipulation of the quantum dot, in the
limiting case of ultra short pulses. Then we discuss the phonon properties for
an excitation with finite pulses. Within a generating function formalism we
calculate the corre- sponding fluctuation properties of the phonons and show
that phonon squeezing can be achieved by the optical manipulation of the
quantum dot exciton for certain conditions even for a single pulse excitation
where neither for short nor for long pulses squeezing occurs. To explain the
occurrence of squeezing we employ a Wigner function picture providing a
detailed understanding of the induced quantum dynamics.
