  Robust engineering of phonon squeezed states in optically excited solids has
emerged as a promising tool to control and manipulate their properties.
However, in contrast to quantum optical systems, detection of phonon squeezing
is subtle and elusive, and an important question is what constitutes an
unambiguous signature of it. The state of the art involves observing
oscillations at twice the phonon frequency in time resolved measurements of the
out of equilibrium phonon fluctuation. Using Keldysh formalism we show that
such a signal is a necessary but not a sufficient signature of a squeezed
phonon, since we identify several mechanisms that do not involve squeezing and
yet which produce similar oscillations. We show that a reliable detection
requires a time and frequency resolved measurement of the phonon spectral
function.
