Squeezed Phonon States And The Spueezing Effect Of Acoustic Phonons

It is well known that squeezedq states as non-classical states have lower quantum fluctuation in one quadrature than that in a coherent or vacuum state, while another quadrature is greater. The idea of the squeezing states can be used to reduce quantum noise in measuring high precise signal. So the research of the squeezing states of Bose has been the important research subject of physics research field.We know phonons that are quasi-particles describe the collective displacements of very many atoms in a crystal. Phonons are elementary particles. We could explain much characteristic of crystals by studying phonons. At low enough temperatures, quantum fluctuations become dominant, which effect observable quantity. So we discuss squeezed phonon states. By phonon parametric process and second-order Raman scattering, phonon squeezed states are generated. Phonons have complicated dispersion relations which generally have several acoustic and optical branches, the phonons in acoustic branches called acoustic phonons. The dispersion of acoustic phonons are linear around the center of the first Brillouin zone. We find two phonons which have opposite wave vectors are bound into pairs through effective attractive interaction. The system belongs to a new state, named pairing state, in which the phonon system consists of two parts: the subsystem of bare phonons and the subsystem of paired phonons. The pairing state has some new properties. Our basic pointing in this letter is that the phonon system in pairing state is in a squeezed state. The noise of one quadrature phase in the squeezed state can below the noise level in the vacuum state while the other quadrature phase has a correspondingly increased variance. The squeezing effect is a temperature-dependent ordered phase. So we can acquire some useful and novel information abut the material properties.