  We investigate experimentally both the amplitude and phase channels of the
collective modes in the quasi-1D charge-density-wave (CDW) system, K0.3MoO3, by
combining (i) optical impulsive-Raman pump-probe and (ii) terahertz time-domain
spectroscopy (THz-TDS), with high resolution and a detailed analysis of the
full complex-valued spectra in both cases. This allows an unequivocal
assignment of the observed bands to CDW modes across the THz range up to 9 THz.
We revise and extend a time-dependent Ginzburg-Landau model to account for the
observed temperature dependence of the modes, where the combination of both
amplitude and phase modes allows one to robustly determine the bare-phonon and
electron-phonon coupling parameters. While the coupling is indeed strongest for
the lowest-energy phonon, dropping sharply for the immediately subsequent
phonons, it grows back significantly for the higher-energy phonons,
demonstrating their important role in driving the CDW formation. We also
include a reassessment of our previous analysis of the lowest-lying phase
modes, whereby assuming weaker electronic damping for the phase channel results
in a qualitative picture more consistent with quantum-mechanical treatments of
the collective modes, with a strongly coupled amplitudon and phason as the
lowest modes.
