  Recent theoretical and experimental work has suggested the tantalizing
possibility of opening a topological gap upon driving the surface states of a
three-dimensional strong topological insulator (TI) with circularly polarized
light. With this motivation, we study the response of TIs to a driving field
that couples to states near the surface. We unexpectedly find coherent
oscillations between the surface and the bulk and trace their appearance to
unavoidable resonances caused by photon absorption from the drive. We show how
these resonant oscillations may be captured by the Demkov- Osherov model of
multi-level Landau-Zener physics, leading to non-trivial consequences such as
the loss of adiabaticity upon slow ramping of the amplitude. We numerically
demonstrate that these oscillations are observable in the time-dependent Wigner
distribution, which is directly measurable in time-resolved ARPES experiments.
Our results apply generically to any system with surface states in the presence
of a gapped bulk, and thus suggest experimental signatures of a novel
surface-bulk coupling mechanism that is fundamental for proposals to engineer
non-trivial states by periodic driving.
