Gap Inhomogeneity in Cuprates: a view from Two-Dimensional Josephson Echo Spectroscopy

Recent advances in the theory of two-dimensional THz spectroscopy of collective excitations have linked spectroscopic signatures to microscopic static disorder. We employ this framework to analyze the recently measured Josephson echo response. The electronic gap inhomogeneity measured with STM is converted into spatial fluctuations of the superfluid density, which seed a predictive calculation of the 2D-THz echo peaks. The measured peak structure is quantitatively reproduced, supporting a minimal scenario where superconducting gap fluctuations alone account for the echo phenomenology, with no signatures of competing local orders. Finally, by modeling the temperature evolution of the Josephson-plasmon linewidth, we attribute the residual damping at low temperatures to inelastic scattering from nodal quasiparticles. This establishes a quantitative bridge between real-space electronic gap disorder and nonlinear THz observables in the cuprates, paving the way to extend this technique to other phases in which competing local orders have been postulated.