  Using the microscopic nonlinear quantum theory of interaction of strong
coherent electromagnetic radiation with a gapped bilayer graphene is developed
for high harmonic generation at low-energy photon excitation-induced Lifshitz
transitions. The Liouville-von Neumann equation for the density matrix is
solved numerically at the nonadiabatic multiphoton excitation regime. By
numerical solutions, we examine the rates of the second and third harmonics
generation at the particle-hole annihilation in induced Lifshitz transitions by
the two linearly polarized coherent electromagnetic waves propagating in
opposite directions. The obtained results show that the gapped bilayer graphene
can serve as an effective medium for generation of even and odd high harmonics
in the sub-THz domain of frequencies.
