Metal-graphene-metal hybrid structures allow angstrom-scale van derWaals gaps, across which electron tunneling occurs. We squeeze terahertz electromagnetic waves through these lambda/10000000 gaps, accompanied by giant field enhancements. Unprecedented transmission reduction of 97% is achieved with the transient voltage across the gap saturating at 5 V. Electron tunneling facilitated by the transient electric field strongly modifies the gap index, starting a self-limiting process related to the barrier height. Our work enables greater interplay between classical optics and quantum tunneling, and provides optical indices to the van der Waals gaps.