# Squeezed Phonons via Second Order Raman Scattering

A stimulated second-order Raman scattering process. The subscript **k**1
(**k**2) represents the higher- (lower-) energy
incident coherent photons. The arrows show the directions of the corresponding
photon and phonon momenta. The incoming coherent photon beams are about
parallel to each other. The actual physical process is as follows: an incident
photon in mode **k**1 interacts with a solid, producing
two acoustic phonons, and leaves in mode **k**2.
For appropriate choice of initial phtoon and phonon states, the acoustic
phonons can be in a two-mode squeezed state. Notice that there are also
additional incoming photons in mode **k**2, therefore
this mode becomes stronger after the interaction, at the expense of mode
**k**1. Also notice that the vector sum of the
two phonon momenta is the difference of the input and output photon momentum
vectors. Since photon wave vectors are generally much smaller than the
phonon ones |**k***i*| << |**q***s*|,
the two acoustic phonon modes have nearly opposite wave vectors ±**q***s*.
This figure is not to scale. The appropriate scale in the figure would
make all four lines of photons and phonons vertical and almost parallel
with each other. For the sake of clarity, we have increased the angle between
them.

Image Source: X. Hu, *Quantum Fluctuations In Condensed Matter Systems*,
UM Ph.D. Thesis, 1997, Page 59.

X. Hu and F. Nori, UM Preprint, 1995; *Physical
Review Letters 76*, 2294 (1996); *Physical Review Letters 79*,
4605 (1997).