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In solid-state physics, the quantized lattice vibrations, i.e., the phonons, play a vital role. Phonons, much like photons, satisfy bosonic commutation relations, and therefore, various concepts well-known in quantum optics can be transferred to the emerging field of phononics. Examples are non-classical states and, in particular, squeezed states. We discuss the generation of phonon squeezing by optically exciting a quantum dot and show that by excitation with detuned continuous wave laser fields, sequences of squeezed phonon wave packets are created, which are emitted from the quantum dot region into the surrounding material.