Electric-field-dependent dielectric constant and nonlinear susceptibility in SrTiO3

${\mathrm{SrTiO}}_{3}$ belongs to the class of incipient ferroelectrics in which an electrically ordered state is suppressed by quantum fluctuations. To investigate the nature of these excitations, we have measured the linear and nonlinear susceptibilities of ${\mathrm{SrTiO}}_{3}$ as a function of temperature T and field E. The application of large fields E counteracts the fluctuations and forces the system into an ordered state. The (E,T) diagram is presented. The field dependence of the dielectric constant can be well described within an Ising model including quantum tunneling. Minima in the third harmonic susceptibility, which is a measure of ferroelectric correlations, are taken as evidence for the onset of coherent tunneling phenomena near T=33 K.