  We propose a robust localization of the highly-excited Rydberg atoms,
interacting with doughnut-shaped optical vortices. Compared with the earlier
standing-wave (SW)-based localization methods, a vortex beam can provide an
ultrahigh-precision two-dimensional localization solely in the zero-intensity
center, within a confined excitation region down to the nanometer scale. We
show that the presence of the Rydberg-Rydberg interaction permits
counter-intuitively much stronger confinement towards a high spatial resolution
when it is partially compensated by a suitable detuning. In addition, applying
an auxiliary SW modulation to the two-photon detuning allows a
three-dimensional confinement of Rydberg atoms. In this case, the vortex field
provides a transverse confinement while the SW modulation of the two-photon
detuning localizes the Rydberg atoms longitudinally. To develop a new
subwavelength localization technique, our results pave one-step closer to
reduce excitation volumes to the level of a few nanometers, representing a
feasible implementation for the future experimental applications.
