RESUMEN
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 ultraprecise 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 a path one step closer to reducing excitation volumes to the level of a few nanometers, representing a feasible implementation for the future experimental applications.