  The anharmonic response of charge-density wave (CDW) order to strong
laser-pulse perturbations in 1T-TaS_2 and TbTe_3 is investigated by means of a
multiple-pump-pulse time-resolved femtosecond optical spectroscopy. We observe
remarkable anharmonic effects hitherto undetected in the systems exhibiting
collective charge ordering. The efficiency for additional excitation of the
amplitude mode by a laser pulse becomes periodically modulated after the mode
is strongly excited into a coherently oscillating state. A similar effect is
observed also for some other phonons, where the cross-modulation at the
amplitude-mode frequency indicates anharmonic interaction of those phonons with
the amplitude mode. By analyzing the observed phenomena in the framework of
time-dependent Ginzburg-Landau theory we attribute the effects to the
anharmonicity of the mode potentials inherent to the broken symmetry state of
the CDW systems.
