  Nanotechnology enables in principle a precise mapping from design to device
but relied so far on human intuition and simple optimizations. In
nanophotonics, a central question is how to make devices in which the
light-matter interaction strength is limited only by materials and
nanofabrication. Here, we integrate measured fabrication constraints into
topology optimization, aiming for the strongest possible light-matter
interaction in a compact silicon membrane, demonstrating an unprecedented
photonic nanocavity with a mode volume of $V\sim3\times10^{-4}\,\lambda^3$,
quality factor $Q\sim1100$, and footprint $4\,\lambda^2$ for telecom photons
with a $\lambda\sim 1550$ nm wavelength. We fabricate the cavity, which
confines photons inside 8 nm silicon bridges and use near-field optical
measurements to perform the first experimental demonstration of photon
confinement to a single hotspot well below the diffraction limit in
dielectrics.
