Quantum materials, systems in which quantum effects lead to unique macroscopic phenomena with tremendous technological potential, comprise the forefront of condensed matter physics research. In particular, collective excitations associated with broken-symmetry phases have attracted tremendous attention as powerful windows into their microscopic physics and dynamics. However, spectroscopy of these collective excitations has been hindered by the so-called ‘terahertz gap’, which refers to difficulties in generation and detection of radiation in the terahertz frequency range, where many relevant modes of quantum materials are found.
 
In response to this challenge, we translate a technique known as 2-D spectroscopy, an optical analogue of multi-dimensional NMR spectroscopy, into the terahertz frequency range. We implement, for the first time to our knowledge, 2-D Terahertz Spectroscopy in a non-collinear, reflection geometry, enabling study of opaque materials and isolation of their constituent terahertz nonlinearities. We apply this technique to the Josephson plasma resonance in La2-xSrxCuO4, a layered high-temperature superconductor, to distill the underlying plasmon correlations and reveal a disordered superconducting state. Measurements of the superconducting transition then provide evidence of an unconventional phase-disordering transition without pair breaking. I will conclude with an outlook for light-induced phase transitions.