  Photo-induced phase transitions have been intensively studied owing to the
ability to control a material of interest in the ultrafast manner, which can
induce exotic phases unable to be attained at equilibrium. However, the key
mechanisms are still under debate, and it has currently been a central issue
how the couplings between the electron, lattice, and spin degrees of freedom
are evolving during photo-induced phase transitions. Here, we develop a new
analysis method, frequency-domain angle-resolved photoemission spectroscopy, to
gain precise insight into electron-phonon couplings during photo-induced
insulator-to-metal transitions for Ta$_2$NiSe$_5$. We demonstrate that multiple
coherent phonons generated by displacive excitations show band-selective
coupling to the electrons. Furthermore, we find that the lattice modulation
corresponding to the 2 THz phonon mode, where Ta lattice is sheared along the
a-axis, is the most relevant for the photo-induced semimetallic state.
