Two-dimensional spatial solitons in optical lattices with Rydberg-Rydberg interaction

Realizing stable high dimensional light solitons is a long-standing goal in the study of nonlinear optical physics. However, in high-dimension space, the light fields will inevitably distorted due to the diffraction. In order to solve the diffraction effect in nonlinear Kerr media and achieve the spatial localization of light fields, we addressed a scheme to generate stable two-dimensional (2D) solitons in a cold Rydberg atomic system with a Bessel optical lattices, where a three-level atomic structure, a weak probe laser field, a strong control field constitute the Rydberg-dressed ladder atomic system. The probe field can be localized when the balance is achieved between local nonlinearity, Bessel potential, and nonlocal nonlinearity which is contributed by the long-range Rydberg-Rydberg interaction (RRI) between Rydberg atoms. Under electric-dipole and rotating-wave approximations, the stable solution of probe field is obtained by solving Maxwell-Bloch equations numerically. A cluster of 2D spatial solitons, including fundamental, two-pole, quadrupole as well as vortex solitons, are found in this system. Among them, the fundamental, two-pole and quadrupole ones have, respectively, one, two, and four intensity centers and no vertical characteristics. On the other hand, the vortex solitons behavior vertical characters in profiles and phase structures. The formation and transportation of these solitons can be controlled by propagation coefficient, the degree of nonlocal nonlinearity and Bessel lattice strength. The stability regions of these solitons are evaluated by anti Vakhitov Kolokolov（ anti-VK） criterion and linear stability analysis method. We found that all of these four kinds of solitons can be generated and stably propagate in space. Owing to the different structures of poles, the states in the transportation are different: the fundamental and vortex ones maintain stable, while the quadrupole ones are mostly unstable. In the modulation of solitons, there is a cutoff value of propagation constant b_co, only bellow which solitons can propagate stably. The light intensity of solitons shows a periodic behavior with Bessel lattice strength. The change period decreases with the order of the solitons as a result of the interaction between the poles. We also found that the solitons are more stable with weak nonlocal nonlinearity coefficient. This study provides a new idea for the generation and regulation of optical solitons in high dimensional space.