Bright Optical Eigenmode of 1 nm^{3} Mode Volume.

We report on the discovery and rationale to devise bright single optical eigenmodes that feature quantum-optical mode volumes of about $1\text{ }\text{ }{\mathrm{nm}}^{3}$. Our findings rely on the development and application of a quasinormal mode theory that self-consistently treats fields and electron nonlocality, spill-out, and Landau damping around atomistic protrusions on a metallic nanoantenna. By outpacing Landau damping with radiation via properly designed antenna modes, the extremely localized modes become bright with radiation efficiencies reaching 30% and could provide up to $4\ifmmode\times\else\texttimes\fi{}{10}^{7}$ times intensity enhancement.