Fig. 4: Density matrix calculations and resulting Wigner phase-space probability distributions for TR-SFX experimental conditions on rsKiiro using different pulse schemes.

Calculations were performed using the parameters listed in Supplementary Table 11, which are representative of the TR-SFX conditions and use the methodology described in Supplementary Section 13. a,b, Comparison of the populations (a(i) and b(i)) and coherences (a(ii) and b(ii)) of the S₀ (red) and S₁ (yellow) electronic states over time, with the pump (dashed lines) and pump–dump (solid lines) schemes shown, for 350-fs pump–dump delay (a, corresponding to Figs. 2 and 3a) and 2-ps delay (b, corresponding to Fig. 3b). A coherence comparison is made between the pump and short 350-fs (a) and long 2-ps (b) pump–dump delays. The Wigner phase-space distributions of the S₀ ground state for all pulse schemes are shown in a(iii) and b(iii), with a(iii) showing an increase in asymmetry due to Tannor–Rice coherence transfer from excited to ground state after dump interaction within vibrational dephasing. In contrast, as expected, the longer 2-ps delay after vibrational dephasing in b(iii) shows minimal impact on the distribution, with a small generation of position (q) and no impulse momentum (p) transferred, but with population transfer after the dump interaction. The corresponding Wigner transformations for S₁ are shown in Supplementary Fig. 58 using surface representations.