Bessel optical lattice is a non-spatially periodic column-symmetric optical lattice potential field, which has the characteristics of infinite deep potential well and ring-shaped potential well. A deep potential is formed in the center of the 0-order Bessel optical lattice. In the non-zero-order Beseel optical lattice, a ring-shaped shallow potential well with a central barrier can be formed. Exciton-polariton is a semi-light and semi-matter quasi-particle, which can achieve the Bose-Einstein condensate phase transition even be at room temperature to form polariton condensates. In addition, the polariton condensates is the possibility to realize in it sufficiently strong spin-orbit coupling originating in the cavity-induced TE-TM splitting of the polariton energy levels. The polariton condensate can be realized at room temperature, and there can be spin-orbit coupling in it, which provides a new platform for the study of quantum physics.
In this paper, the Bessel optical lattice is introduced into polariton condensate. The stationary state structures of spinor two-component polariton condensates with spin-orbit coupling are investigated. By solving the Gross-Pitaevskii equation, we first give the stationary state structures of the polariton condensate in the laboratory coordinate frame and the rotating coordinate frame. Due to the introduction of the Bessel optical lattice, the stationary state structures of polariton condensate are diverse. We dispaly the stationary state structures of the basic Gaussian solitons and multipole solitons in the central deep potential well in the laboratory coordinate frame, and the ring solitons and multipole solitons in the central shallow potential well. We also dispaly the vortex ring soliton that exists in the rotating coordinate frame, and the stationary state structure of the component separation caused by the spin-orbit interaction. We analyzed the influence of the spin-orbit coupling on the stationary state structures in the two coordinate frames, and also analyzed the stability of the multipole solitons in the rotating coordinate frame. It is found that the multipole solitons formed in the ring-shaped shallow potential well have better stability than the multipole solitons formed in the central deep potential well, and they can maintain the relative structure and spatial distribution for a long time during the rotation process. In the rotating coordinate frame, even if the two-component separation conditions are not satisfied, the introduction of spin-orbit coupling can cause the two components to separate.
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