Ultrafast Two-Dimensional Spectroscopy Uncovers Ubiquitous Electron-Paramagnon Coupling in Cuprate Superconductors

The coupling between electronic excitations and collective bosonic modes is fundamental to the emergence of high-temperature superconductivity in cuprates. Despite extensive effort, conventional equilibrium and pump-probe optical spectroscopies still struggle to disentangle couplings to different bosonic modes when their energy scales overlap. Here we overcome this limitation using ultrafast two-dimensional electronic spectroscopy (2DES), which correlates coherent excitation and detection photon energies with femtosecond time resolution. Applied to optimally doped Bi$_2$Sr$_2$Ca$_{0.92}$Y$_{0.08}$Cu$_2$O$_{8+\delta}$, 2DES reveals a pronounced off-diagonal resonance arising from the ultrafast generation of non-thermal bosons with energy $\hbar\Omega_\mathbf{q}\simeq200$ meV. By comparing the measured spectra with a theoretical framework that explicitly includes the interaction between charge-transfer and magnetic excitations, we identify these bosons as paramagnons with momenta centered near $(\pi/2,\pi/2)$ and extending toward $(0,\pi)$ and $(\pi,0)$. The resonance persists across a large range of temperatures and doping concentrations, demonstrating that high-energy paramagnons are ubiquitously and strongly coupled to electronic excitations throughout the cuprate phase diagram. Time-domain analysis constrains the build-up of the paramagnon population to $\lesssim 10$ fs, placing a lower bound $\lambda \gtrsim 0.7$ on the coupling strength. More broadly, our results establish 2DES as a powerful approach for disentangling mode-selective electron-boson interactions and addressing decoherence dynamics, thereby establishing a new avenue for investigating strongly correlated quantum materials. These findings also provide a direct framework for future time-resolved resonant inelastic X-ray scattering experiments aimed at tracking the ultrafast dynamics of magnetic excitations.