A charged particle modifies the structure of the surrounding medium: examples include a proton in ice1, an ion in a DNA molecule2, an electron at an interface3, or an electron in an organic4 or inorganic crystal5, 6, 7. In turn, the medium acts back on the particle. In a polar or ionic solid, a free electron distorts the crystal lattice, displacing the atoms from their equilibrium positions. The electron, when considered together with its surrounding lattice distortion, is a single quasiparticle5, 6, known as the Fröhlich polaron8, 9. The basic properties of polarons and their drift motion in a weak electric field are well known10, 11, 12. However, their nonlinear high-field properties—relevant for transport on nanometre length and ultrashort timescales—are not understood. Here we show that a high electric field in the terahertz range drives the polaron in a GaAs crystal into a highly nonlinear regime where, in addition to the drift motion, the electron is impulsively moved away from the centre of the surrounding lattice distortion. In this way, coherent lattice vibrations (phonons) and concomitant drift velocity oscillations are induced that persist for several hundred femtoseconds. They modulate the optical response at infrared frequencies between absorption and stimulated emission. Such quantum coherent processes directly affect high-frequency transport in nanostructures and may be exploited in novel terahertz-driven optical modulators and switches.