  Intense, single-cycle terahertz (THz) pulses offer a promising approach for
understanding and controlling the properties of a material on an ultrafast time
scale. In particular, resonantly exciting phonons leads to a better
understanding of how they couple to other degrees of freedom in the material
(e.g., ferroelectricity, conductivity and magnetism) while enabling coherent
control of lattice vibrations and the symmetry changes associated with them.
However, an ultrafast method for observing the resulting structural changes at
the atomic scale is essential for studying phonon dynamics. A simple approach
for doing this is optical second harmonic generation (SHG), a technique with
remarkable sensitivity to crystalline symmetry in the bulk of a material as
well as at surfaces and interfaces. This makes SHG an ideal method for probing
phonon dynamics in topological insulators (TI), materials with unique surface
transport properties. Here, we resonantly excite a polar phonon mode in the
canonical TI Bi$_2$Se$_3$ with intense THz pulses and probe the subsequent
response with SHG. This enables us to separate the photoinduced lattice
dynamics at the surface from transient inversion symmetry breaking in the bulk.
Furthermore, we coherently control the phonon oscillations by varying the time
delay between a pair of driving THz pulses. Our work thus demonstrates a
versatile, table-top tool for probing and controlling ultrafast phonon dynamics
in materials, particularly at surfaces and interfaces, such as that between a
TI and a magnetic material, where exotic new states of matter are predicted to
exist.
