  The coherence of collective modes, such as phonons, and their modulation of
the electronic states are long sought in complex systems, which is a
cross-cutting issue in photovoltaics and quantum electronics. In photovoltaic
cells and lasers based on metal halide perovskites, the presence of polaronic
coupling, i.e., photocarriers dressed by the macroscopic motion of charged
lattice, assisted by terahertz (THz) longitudinal optical (LO) phonons, has
been intensely studied yet still debated. This may be key for explaining the
remarkable properties of the perovskite materials, e.g., defect tolerance, long
charge lifetimes and diffusion length. Here we use the intense single-cycle THz
pulse with the peak electric field up to $E_{THz}=$1000\,kV/cm to drive
coherent band-edge oscillations at room temperature in CH$_3$NH$_3$PbI$_3$. We
reveal the oscillatory behavior dominantly to a specific quantized lattice
vibration mode at $\omega_{\mathrm{LO}}\sim$4 THz, being both dipole and
momentum forbidden. THz-driven coherent dynamics exhibits distinguishing
features: the room temperature coherent oscillations at $\omega_{\mathrm{LO}}$
longer than 1 ps in both single crystals and thin films; the {\em
mode-selective} modulation of different band edge states assisted by
electron-phonon ($e$-$ph$) interaction; {\em dynamic mode splitting} controlled
by temperature due to entropy and anharmonicity of organic cations. Our results
demonstrate intense THz-driven coherent band-edge modulation as a powerful
probe of electron-lattice coupling phenomena and provide compelling
implications for polaron correlations in perovskites.
