  It is of fundamental interest in controlling the light-matter interaction for
a long time in the field of quantum information processing. However, usual
excitation with the propagating photon can hardly excite a localized state of
light while keeping the atom under a subradiant decay in an atom-waveguide
system. Here, we propose a model of coupling between a giant atom and the
dynamically-modulated coupled-resonator waveguide and find that a bound state,
where the light shows the localization effect and atom exhibits a subradiant
decay time, can be excited by a propagating photon. An analytical treatment
based on the separation of the propagating states and localized states of light
has been used and provides inspiring explanation of our finding, i.e., a
propagating photon can be efficiently converted to the localized light through
the light-atom interactions in three resonators at frequency difference
precisely equivalent to external modulation frequency. Our work therefore
provides an alternative method for actively localizing the photon in a
modulated coupled-resonator waveguide system interacting with giant atom, and
also points out a way to study the light-atom interaction in a synthetic
frequency dimension that holds the similar Hamiltonian.
