Detection of squeezed phonons in pump-probe spectroscopy

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 the 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 produce similar oscillations. We show that reliable detection requires a time- and frequency-resolved measurement of the phonon spectral function.