Nonclassical states of lattice excitations: squeezed and entangled phonons

We consider theoretical and experimental evidence for nonclassical states of a crystal lattice. Our primary goal is the critical analysis of recent experiments in which squeezed and entangled phonons are created and investigated. The quantum aspects of elastic deformation fields similar to nonclassical light fields are of interest for potential use in applied and fundamental research, including quantum computing and testing various hypotheses in quantum physics.