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Resonant inelastic x-ray scattering (RIXS) has become an important tool forstudying elementary excitations in correlated materials. Here, we present asystematic theoretical investigation of the Cu L-edge RIXS spectra of undopedand doped cuprate two-leg spin-ladders in both the non-spin-conserving (NSC)and spin-conserving (SC) channels. The spectra are rich and host many exoticexcitations. In the NSC-channel of the undoped case, we identify one-triplonand bound $\textit{triplet}$ two-triplon excitations in the strong-rungcoupling limit, as well as confined spinons in the weak-rung coupling limit. Inthe doped case, we observe a quasiparticle excitation formed from a boundcharge and spin-$\frac{1}{2}$ in the strong-rung coupling limit. In theSC-channel, we also identify several new features, including bound$\textit{singlet}$ two-triplon excitations and confined spinons in the undopedladders in the strong- and weak-rung coupling limits, respectively. Conversely,in the doped case, the SC channel primarily probes both gapless and gappedcharge excitations. Finally, we revisit the available data for the laddercompound Sr$_{14}$Cu$_{24}$O$_{41}$ in the context of our results.

Theoretical study of the spin and charge dynamics of two-leg ladders as probed by resonant inelastic x-ray scattering