Theory of symmetry-resolved quench-drive spectroscopy: Nonlinear response of phase-fluctuating superconductors

Recent experiments on cuprates have shown the possibility of opening a gap above the superconducting critical temperature, in the so-called phase-fluctuating state, by enhancing the phase coherence of preformed Cooper pairs. Quench-drive spectroscopy, an implementation of 2D coherent spectroscopy, has emerged as a powerful tool for investigating out-of-equilibrium superconductors and their collective modes. In this work, we enrich the quench-drive scheme by developing a systematic generalization to study the nonlinear response of $d$-wave incoherent Cooper pairs in a symmetry resolved manner. In particular, we do not only show that it is possible to obtain a third harmonic signal from fully incoherent pairs with an equilibrium vanishing order parameter, but we also characterize the full flourishing 2D spectrum of the generated nonlinear response. The results provide a deeper theoretical insight on recent experimental results, opening the door to a new symmetry-driven design of future experiments on unconventional and enhanced superconductors.