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

We theoretically investigate the out-of-equilibrium dynamics in a binary Bose-Einstein condensate confined within two-dimensional box potentials. One species of the condensate interacts with a pair of oppositely wound, but otherwise identical Laguerre-Gaussian laser pulses, while the other species is influenced only via the interspecies interaction. Starting from the Hamiltonian, we derive the equations of motion that accurately delineate the behavior of the condensates during and after the light-matter interaction. Depending on the number the helical windings (or the magnitude of topological charge), the species directly participating in the interaction with lasers is dynamically segmented into distinct parts which collide together as the pulses gradually diminish. This collision event generates nonlinear structures in the related species, coupled with the complementary structures produced in the other species, due to the interspecies interaction. The long-time dynamics of the optically perturbed species is found to develop the Kolmogorov-Saffman scaling law in the incompressible kinetic energy spectrum, a characteristic feature of the quantum turbulent state. However, the same scaling law is not definitively exhibited in the other species. This study warrants the usage of Laguerre-Gaussian beams for future experiments on quantum turbulence in Bose-Einstein condensates.