Detection of a two-phonon mode in a cuprate superconductor via polarimetric RIXS

Recent improvements in the energy resolution of resonant inelastic x-ray scattering experiments (RIXS) at the Cu-L$_3$ edge have enabled the study of lattice, spin, and charge excitations. Here, we report on the detection of a low intensity signal at 140meV, twice the energy of the bond-stretching (BS) phonon mode, in the cuprate superconductor $\textrm{Bi}_2\textrm{Sr}_2\textrm{Ca}\textrm{Cu}_2\textrm{O}_{8+x}$ (Bi-2212). Ultra-high resolution polarimetric RIXS measurements allow us to resolve the outgoing polarization of the signal and identify this feature as a two-phonon excitation. Further, we study the connection between the two-phonon mode and the BS one-phonon mode by constructing a joint density of states toy model that reproduces the key features of the data.