Electro-optic cavities for in-situ measurement of cavity fields.

Cavity electrodynamics offers a unique avenue for tailoring ground-state material properties, excited-state engineering, and versatile control of quantum matter. Merging these concepts with high-field physics in the terahertz (THz) spectral range opens the door to explore low-energy, field-driven cavity electrodynamics, emerging from fundamental resonances or order parameters. Despite this demand, leveraging the full potential of field-driven material control in cavities is hindered by the lack of direct access to the intra-cavity fields. Here, we demonstrate a new concept of active cavities, consisting of electro-optic Fabry-Pérot resonators, which measure their intra-cavity electric fields on sub-cycle timescales. We thereby demonstrate quantitative retrieval of the cavity modes in amplitude and phase, over a broad THz frequency range. To enable simultaneous intra-cavity sampling alongside excited-state material control, we design a tunable multi-layer cavity, enabling deterministic design of hybrid cavities for polaritonic systems. Our theoretical models reveal the origin of the avoided crossings embedded in the intricate mode dispersion, and will enable fully-switchable polaritonic effects within arbitrary materials hosted by the hybrid cavity. Electro-optic cavities (EOCs) will therefore serve as integrated probes of light-matter interactions across all coupling regimes, laying the foundation for field-resolved intra-cavity quantum electrodynamics.