Inhomogeneities crucially influence the properties of quantum materials, yet methods that can measure them remain limited and can access only a fraction of relevant observables. For example, local probes such as scanning tunnelling microscopy have documented that the electronic properties of cuprate superconductors are inhomogeneous over nanometre length scales. However, complementary techniques that can resolve higher-order correlations are needed to elucidate the nature of these inhomogeneities. Furthermore, local tunnelling probes are often effective only far below the critical temperature. Here we develop a two-dimensional terahertz spectroscopy method to measure Josephson plasmon echoes from an interlayer superconducting tunnelling resonance in a near-optimally doped cuprate. The technique allows us to study the multidimensional optical response of the interlayer Josephson coupling in the material and disentangle intrinsic lifetime broadening from extrinsic inhomogeneous broadening for interlayer superconducting tunnelling. We find that inhomogeneous broadening persists up to a substantial fraction of the critical temperature, above which this is overcome by the thermally increased lifetime broadening.

不均匀性对量子材料的特性产生至关重要的影响，但测量它们的方法仍然有限，并且只能获取一小部分相关的可观测值。例如，扫描隧道显微镜等局部探针已证明铜酸盐超导体的电子特性在纳米长度尺度上是不均匀的。然而，需要能够解决高阶相关性的补充技术来阐明这些不均匀性的本质。此外，局部隧道探针通常仅在远低于临界温度时有效。在这里，我们开发了一种二维太赫兹光谱方法来测量近乎最佳掺杂铜酸盐中层间超导隧道共振的约瑟夫森等离子体回波。该技术使我们能够研究材料中层间约瑟夫森耦合的多维光学响应，并将本征寿命展宽与层间超导隧道效应的外在非均匀展宽分开。我们发现，不均匀展宽持续到临界温度的很大一部分，高于该温度，可以通过热增加的寿命展宽来克服这一问题。