Fig. 4: Testing the hypothesis of the phonon-assisted electronic order formation by using two pump-pulses.

a Typical time-resolved total displacement \({A}_{{{{{{{\mathrm{tot}}}}}}}}/{A}_{{{{{{{\mathrm{tot}}}}}}},{{{{{{\mathrm{GS}}}}}}}}\) normalized by its value in the ground state for two pump pulses arriving as indicated. The second pulse changes the phonon amplitude²⁹. b The density wave recovery time, τ, as a function of the phonon amplitude, \({A}_{{{{{{{\mathrm{ph}}}}}}}}{/A}_{\psi ,{{{{{{\mathrm{GS}}}}}}}}\) normalized by the order parameter in the ground state, both measured after the arrival of the second pump pulse. Each pair of values is determined from a fit to the data measured with a fixed time delay between the two pump pulses; the analysis procedure is identical to the analysis used for single-pulse data (see Eq. (1)), with taking the arrival of the second pulse as time zero. The red line shows a linear fit with \(\tau \left({A}_{{{{{{\rm{ph}}}}}}}/{A}_{\psi ,{{{{{{\mathrm{GS}}}}}}}}\right)=b\left({A}_{{{{{{\rm{ph}}}}}}}/{A}_{\psi ,{{{{{{\mathrm{GS}}}}}}}}\right)+c\), with \(b=-0.046\) and \(c=0.35\). The dashed gray lines indicate the prediction intervals of the fit. Inset: The quench after the second pulse as a function of the phonon amplitude: the second pulse induces the same quench independent of the phonon amplitude. All pump-pump delays are larger than 0.5 ps, ensuring the electron-lattice equilibration completes before the second pulse arrives. Both pump pulses have the same intensity, 1 mJ/cm², which only partially quenches the spin density wave.