Vortex clusters and their active control in a cold Rydberg atomic system with <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>P</mml:mi> <mml:mi>T</mml:mi> </mml:mrow> </mml:math> -symmetric Bessel potential

Abstract We propose an approach for generating robust two-dimensional (2D) vortex clusters (VCs) in a Rydberg atomic system by utilizing parity-time ( <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mi mathvariant="script">P</mml:mi> <mml:mi mathvariant="script">T</mml:mi> </mml:mrow> </mml:math> ) symmetric optical Bessel potential. We show that the system supports novel multi-core VCs with four and eight cores, corresponding to topological charges 2 and 4, respectively. The stability of these VCs can be dynamically adjusted through the manipulation of the gain-loss component, Kerr nonlinearities, and the degree of nonlocality inherent in the Rydberg atoms. These VCs are confined within the first lattice well of the Bessel potential, and both the power and width of lights undergo a quasi-periodic breathing phenomenon, which is attributed to the power exchange between the light fields and Bessel potential. Both self-attractive and self-repulsive Kerr interactions can sustain robust VCs within this system. The insights presented here not only facilitate the creation and manipulation of 2D VCs through <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mi mathvariant="script">P</mml:mi> <mml:mi mathvariant="script">T</mml:mi> </mml:mrow> </mml:math> -symmetric potentials but also pave the way for potential applications in optical information processing and transmission.