  Many functionally relevant ferroic phenomena in quantum materials can be
manipulated by driving the lattice coherently with optical and terahertz
pulses. New physical phenomena and non-equilibrium phases that have no
equilibrium counterpart have been discovered following these protocols. The
underlying structural dynamics has been mostly studied by recording the average
atomic position along dynamical structural coordinates with elastic scattering
methods. However, crystal lattice fluctuations, which are known to influence
phase transitions in equilibrium, are also expected to determine these dynamics
but have rarely been explored. Here, we study the driven dynamics of the
quantum paraelectric SrTiO3, in which mid-infrared drives have been shown to
induce a metastable ferroelectric state. Crucial in these physics is the
competition between the polar instability and antiferrodistortive rotations,
which in equilibrium frustrate the formation of long-range ferroelectricity. We
make use of high intensity mid-infrared optical pulses to resonantly drive a
Ti-O stretching mode at 17 THz, and we measure the resulting change in lattice
fluctuations using time-resolved x-ray diffuse scattering at a free electron
laser. After a prompt increase, we observe a long-lived quench in R-point
antiferrodistortive lattice fluctuations. The enhancement and reduction in
lattice fluctuations are explained theoretically by considering fourth-order
nonlinear phononic interactions and third-order coupling to the driven optical
phonon and to lattice strain, respectively. These observations provide a number
of new and testable hypotheses for the physics of light-induced
ferroelectricity.
