  Femtosecond pulses have been used to reveal hidden broken symmetry states and
induce transitions to metastable states. However, these states are mostly
transient and disappear after laser removal. Photoinduced phase transitions
towards crystalline metastable states with a change of topological order are
rare and difficult to predict and realize experimentally. Here, by using
constrained density functional perturbation theory and accounting for
light-induced quantum anharmonicity, we show that ultra-fast lasers can
permanently transform the topologically-trivial orthorhombic structure of SnSe
into the topological crystalline insulating rocksalt phase via a first-order
non-thermal phase transition. We describe the reaction path and evaluate the
critical fluence and the possible decay channels after photoexcitation. Our
simulations of the photoexcited structural and vibrational properties are in
excellent agreement with recent pump-probe data in the intermediate fluence
regime below the transition with an error on the curvature of the quantum free
energy of the photoexcited state that is smaller than 2%.
