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One-dimensional purely Lee-Huang-Yang fluids dominated by quantum fluctuations in two-component Bose-Einstein condensates

Lee-Huang-Yang (LHY) fluids are an exotic quantum matter dominated purely by quantum fluctuations. Recently, the three-dimensional LHY fluids were observed in ultracold atoms experiments, while their low-dimensional counterparts have not been well known. Herein, based on the Gross-Pitaevskii equation of one-dimensional LHY quantum fluids in two-component Bose-Einstein condensates, we reveal analytically and numerically the formation, properties, and dynamics of matter-wave structures therein. Considering a harmonic trap, approximate analytical results are obtained based on variational approximation, and higher-order nonlinear localized modes with nonzero nodes are constructed numerically. Stability regions of all the LHY nonlinear localized modes are identified by linear-stability analysis and direct perturbed numerical simulations. Movements and oscillations of single localized mode, and collisions between two modes, under the influence of different initial kicks are also studied in dynamical evolutions. The predicted results are available to quantum-gas experiments, providing a new insight into LHY physics in low-dimensional settings.