Title: Phonon dispersion of quantum paraelectric SrTiO3 in electric fields

Abstract: Here we report on an elastic and inelastic neutron scattering study addressing the effect of electric fields on quantum paraelectric SrTiO3. Our elastic scattering results find small changes as a function of field in a superlattice reflection that sample the octahedral rotations, which is indicative of only weak coupling of octahedral rotation and electric polarization. By collecting not only the change in gap, but also of the dispersion, we can better quantify the changes in the lattice dynamics. The findings are put in context to recent field DFT calculations predicting the E-field effect on the atomic motions of the lowest lying transverse optical (soft) mode. We find hints of non-linear coupling to the acoustic mode and to the phonon with polarization perpendicular to the E-field, which shows the non-linearity in the chemical potential that is also relevant when strongly driving SrTiO3 with E-field (THz) pulses.