  Halide perovskites, such as methylammonium lead bromide (MAPbBr$_3$), host
tightly bound three-dimensional excitons which are robust at room temperature.
Excellent optical properties of MAPbBr$_3$ allow for designing of optical
single-mode waveguides and cavities in the frequency range close to the
excitonic transitions. Taken together, this turns MAPbBr$_3$ into an excellent
platform for probing exciton-polariton nonlinear phenomena at room temperature.
Here we investigate ultrafast non-equilibrium dynamics of polaritons under
pulsed fs non-resonant excitation. We demonstrate the presence of the
stimulated acoustic phonon-assisted scattering regime above threshold pump
fluence, characterized by the explosive growth of emission intensity, a
redshift of the emission spectral maximum, spectral narrowing, and
sub-picosecond emission dynamics. Our theoretical findings are well confirmed
by the results of experimental measurements.
