  We outline here how strong light-matter interaction can be used to induce
quantum phase transition between normal and topological phases in
two-dimensional topological insulators. We consider the case of a HgTe quantum
well, in which band inversion occurs above a critical value of the well
thickness, and demonstrate that coupling between electron states and the $E$
field from an off-resonant linearly polarized laser provides a powerful tool to
control topological transitions, even for a thickness of the quantum well that
is below the critical value. We also show that topological phase properties of
the edge states, including their group velocity, can be tuned in a controllable
way by changing the intensity of the laser field. These findings open up the
possibility for new experimental means with which to investigate topological
insulators and shed new light on topological-insulator-based technologies that
are under active discussion.
