Phonon Squeezed States: Quantum Noise Reduction in Solids

This article discusses quantum fluctuation properties of a crystal lattice, and in particular, phonon squeezed states. Squeezed states of phonons allow a reduction in the quantum fluctuations of the atomic displacements to below the zero-point quantum noise level of coherent phonon states. Here we discuss our studies of both continuous-wave and impulsive second-order Raman scattering mechanisms. The later approach was used to experimentally suppress (by one part in a million only, which might be noise) fluctuations in phonons (and it has not been clearly reproduced by other experimental groups). We calculate the expectation values and fluctuations of both the atomic displacement and the lattice amplitude operators, as well as the effects of the phonon squeezed states on macroscopically measurable quantities, such as changes in the dielectric constant. These results are compared with recent experiments. Further information, including preprints and animations, are available in http://www-personal.engin.umich.edu/\~nori/squeezed.html