Fig. 2.

Loop diagrams for single-molecule (Eq. 4) X-ray scattering processes. The shaded area represents an arbitrary excitation that prepares the system in a superposition of $|g⟩$ and $|e⟩$ states (further explained in SI Appendix, Fig. S1). The checkered box represents a field-free propagation period $T$ that separates the state preparation from the X-ray probing process. We denote modes of the X-ray probe pulse with $p$ and $p\prime$, whereas $s$, $s\prime$ represent relevant scattering modes (${\mathbf{k}}_{p^{\left(\prime \right)}}$ has frequency ${\omega }_{p^{\left(\prime \right)}}$ and ${\mathbf{k}}_{s^{\left(\prime \right)}}$ has frequency ${\omega }_{s^{\left(\prime \right)}}$). Elastic scattering processes come with ${\widehat{\sigma }}_{gg}$ or ${\widehat{\sigma }}_{ee}$ and are denoted by black field arrows. Inelastic processes in which the molecule gains (Stokes) or loses (anti-Stokes) energy to the field come with ${\widehat{\sigma }}_{ge}$ or ${\widehat{\sigma }}_{eg}$ depending whether the action is on the ket or bra and are denoted with red and blue field arrows to indicate the field’s spectral shift due to the particular diagram. Note: In C, F, and G, the energy order of states $e,e\prime ,e^{″}$ is not set. We have depicted the elastic cases for specificity. Diagrams A–H identify the corresponding terms in Eq. 13.