The gap in bilayer graphene (BLG) can directly be controlled by a perpendicular electric field. By tuning the field through zero at a finite rate in neutral BLG, excited states are produced. Due to screening, the resulting dynamics is determined by coupled nonlinear Landau-Zener models. The generated defect density agrees with Kibble-Zurek theory in the presence of subleading logarithmic corrections. After the quench, population inversion occurs for wave vectors close to the Dirac point. This could, at least, in principle, provide a coherent source of infrared radiation with tunable spectral properties (frequency and broadening). Cold atoms with quadratic band crossing exhibit the same dynamics.