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We theoretically investigate the out-of-equilibrium dynamics in a binaryBose-Einstein condensate confined within two-dimensional box potentials. Onespecies of the condensate interacts with a pair of oppositely wound, butotherwise identical Laguerre-Gaussian laser pulses, while the other species isinfluenced only via the interspecies interaction. Starting from theHamiltonian, we derive the equations of motion that accurately delineate thebehavior of the condensates during and after the light-matter interaction.Depending on the number the helical windings (or the magnitude of topologicalcharge), the species directly participating in the interaction with lasers isdynamically segmented into distinct parts which collide together as the pulsesgradually diminish. This collision event generates nonlinear structures in therelated species, coupled with the complementary structures produced in theother species, due to the interspecies interaction. The long-time dynamics ofthe optically perturbed species is found to develop the Kolmogorov-Saffmanscaling law in the incompressible kinetic energy spectrum, a characteristicfeature of the quantum turbulent state. However, the same scaling law is notdefinitively exhibited in the other species. This study warrants the usage ofLaguerre-Gaussian beams for future experiments on quantum turbulence inBose-Einstein condensates.

Pattern Formation and Evidence of Quantum Turbulence in Binary Bose-Einstein Condensates Interacting with a Pair of Laguerre-Gaussian Laser Beams