Evolution of coherent collective modes through consecutive CDW transitions in (PO$_{2}$)$_{4}$(WO$_{3}$)$_{12}$ mono-phosphate tungsten bronze

All optical femtosecond relaxation dynamics in a single crystal of mono-phosphate tungsten bronze (PO$_{2}$)$_{4}$(WO$_{3}$)$_{2m}$ with alternate stacking m=6 of WO$_{3}$ layers was studied through the three consequent charge density wave (CDW) transitions. Several transient coherent collective modes associated to the different CDW transitions were observed and analyzed in the framework of the time dependent Ginzburg-Landau theory. Remarkably, the interference of the modes leads to an apparent rectification effect in the transient reflectivity response. A saturation of the coherent-mode amplitudes with increasing pump fluence well below the CDWs destruction threshold fluence indicates a decoupling of the electronic and lattice parts of the order parameter under strong optical drive.