Momentum dispersive spin-excitations in Cu $L_3$-edge resonant inelastic x-ray scattering from Sr$_{14}$Cu$_{24}$O$_{41}$

Using resonant inelastic x-ray scattering (RIXS) at the Cu $L_{3}$ edge in Sr$_{14}$Cu$_{24}$O$_{41}$ we study the dispersion of collective spin excitations in the ladder system along the leg-direction. From calculations within an effective Hubbard model for a finite-size cluster and optical selection rules the observed modes are assigned to two-triplon excitations. Our data reveal a homogeneous cross-section over the full Brillouin zone (BZ). Magnetic quantum fluctuations in the ladders lead to sizable scattering intensity at the $\Gamma$-point, where the two-triplon energy gap is evaluated to 100$\pm$30 meV.