  Optical lattices are the basic blocks of atomic quantum technology. The scale
and resolution of these lattices are diffraction-limited to the light
wavelength. Tight confinement of single sites in conventional lattices requires
excessive laser intensity which in turn suppresses the coherence due to
enhanced scattering. This article proposes a new scheme for atomic optical
lattice with sub-wavelength spatial structure. The potential is formed by the
nonlinear optical response of the three-level Rydberg-dressed atoms, which is
not constrained by the diffraction limit of the driving fields. The lattice
consists of a 3D array of ultra-narrow Lorentzian wells with sub-nanometer
widths. These extreme scales are now optically accessible by a hybrid scheme
deploying the dipolar interaction and optical twist of atomic eigenstates. The
interaction-induced two-body resonance that forms the trapping potential, only
occurs at a peculiar laser intensity, localizing the trap sites to ultra-narrow
regions over the standing-wave driving field. The Lorentzian trapping
potentials with 2\AA width and 30MHz depth are realizable with scattering rates
as low as 1Hz. The spatial correlation between atoms' position at the resonance
points provides a global phononic bus that enables gate operation via the
side-band laser driving similar to the ion-trap schemes. This feature brings
all to all connectivity that unlike the ion counterpart is not limited to
one-dimensional lattices. The ultra-narrow trapping techniques are particularly
demanding for Rydberg-Fermi gates, atomtronics, quantum walks, Hubbard models,
and neutral-atom quantum simulation.
