Abstract
A theoretical framework is presented to investigate the stability of novel two-dimensional quantum droplets within zeroth-order Bessel lattices. The evolution of quantum droplets is studied by the Gross-Pitaevskii equations with Lee-Huang-Yang corrections. The circular groove structure inherent in the zeroth-order Bessel lattice potential facilitates the formation of distinct configurations, including stable zero-vorticity annular quantum droplets and annular quantum droplets featuring embedded vorticity. The stability region of these quantum droplets is achieved through direct numerical simulations. It is found that the lower limit of the stability range for quantum droplets under this optical lattice remains unaffected by vorticity. Conversely, the upper limit exhibits a discernible dependence on vorticity. Subsequently, the study extends to the construction of stable composite states, manifesting as nested concentric multiring structures. Numerical results not only validate the feasibility of nesting vortical quantum droplets under the influence of a zeroth-order Bessel lattice potential but also establish that the vorticity of the smaller droplet within nested vortical quantum droplets does not surpass half of that observed in the larger droplet. Moreover, a comparative analysis highlights the enhanced stability of nested quantum droplets with varying vorticities when contrasted with their counterparts possessing identical vorticities.