Squeezed states of optical phonons in driven ferroelectrics

We analyze the quantum dynamics of dipole-active optical phonons induced by a strong ultrafast driving electric field. We find that the quartic nonlinearity which is universal to optical phonons leads to strong squeezing and efficient parametric generation of dipole-active optical phonons at high wavevectors, even in the presence of damping with rates characteristic of optical phonons in existing ferroelectrics. We further show that the quantum dynamics of the optical phonon mode under driving entails generation of non-Gaussian states of phonons, as a result of the large single-phonon nonlinearity associated with quartic anharmonicities in solids. We illustrate this in the example platform of lithium niobate, a conventional ferroelectric which has relatively weak damping. We further analyze the coupling of driven phonons to light, which leads to the emission far-field terahertz radiation by driven phonons. We specifically analyze the quantum statistics of the radiated photons. We find that these nonlinear phononic interactions imprint a signature in the radiated far-field, for example by the production of squeezed states of light at terahertz frequencies: a frequency range where squeezed light has not yet been realized. Beyond radiation, another important signature of the parametric optical-phonon generation effect we predict is time-dependent modulation of the electronic band-gap of the underlying material, which can be probed by ultrafast pump-probe measurements.