(a) The photo-excited CO dynamics. ΔE is the energy difference with respect to the ground state energy. The grey shaded area represents the total ΔE in the long-ranged CO channel, whereas the red and green areas represent the ΔE contribution of the amplitude and phase, respectively. The dissipation of ΔE through the coupling to the lattice degree of freedom results in the recovery of the CO order parameter and the increase of lattice energy, as indicated by the area below the black dashed line (labelled 'Lattice'). The order parameter completely recovers when the absorbed energy eventually dissipates entirely to the sample environment. Sketches of order parameters at three representative temporal regions are also shown. In each sketch, the red stripes illustrate the CO in real space (that is, the charge stripes) whose order parameter is symbolically drawn below as the red sinusoidal wave. The brightness of the stripe also represents the amplitude of the order parameter. The dashed sinusoidal waves and lines with green and blue colours illustrate the fluctuations of the phase of the CO order parameter. In these sketches, Δ, φ and ξ, respectively represent the amplitude, phase and the phase–phase correlation length of the CO order parameter. (b) Sketches for CO evolution in thermal equilibrium. Near the phase transition temperature TC, in addition to the Gaussian phase fluctuation (green and blue dashed lines), large phase fluctuations also occur and create topological defects (black dot), reducing the coherence length and amplitude of the CO order parameter.