  The system of cold two-level atoms inside an optical lattice potential has
been used to simulate various models encountered in fundamental and
condensed-matter physics. When the optical lattice is periodically shaken, some
interesting dynamical effects were observed. In this work, by utilizing the
ultra-narrow linewidth of the dipole-forbidden transition in $^{87}$Sr atoms
loaded in a shaken optical lattice, we reach a new operation regime where the
shaking rate is much larger than linewidth of the two-level transition but much
smaller than the frequency interval of the harmonic lattice potential, which
was not realizable before. Under such unique conditions, an interesting quantum
dynamical effect, the high-order sideband effect (HSE), has been experimentally
observed. All the results can be well explained by a developed theoretical
model with analytical solution. This HSE is governed by different mechanism as
the similar phenomenon observed in semiconductors and has unique
characteristics.
