Quasi-two-dimensional Bose–Einstein condensates with spatially modulated cubic–quintic nonlinearities

We investigate exact nonlinear matter wave functions with odd and even parities in the framework of quasi-two-dimensional Bose–Einstein condensates (BECs) with spatially modulated cubic–quintic nonlinearities and harmonic potential. The existence condition for these exact solutions requires that the minimum energy eigenvalue of the corresponding linear Schrödinger equation with harmonic potential is the cutoff value of the chemical potential λλ. The competition between two-body and three-body interactions influences the energy of the localized state. For attractive two-body and three-body interactions, the larger the matter wave order number nn, the larger the energy of the corresponding localized state. A linear stability analysis and direct simulations with initial white noise demonstrate that, for the same state (fixed nn), increasing the number of atoms can add stability. A quasi-stable ground-state matter wave is also found for repulsive two-body and three-body interactions. We also discuss the experimental realization of these results in future experiments. These results are of particular significance to matter wave management in higher-dimensional BECs.

► 2D Bose–Einstein condensates (BECs) with spatially modulated cubic–quintic nonlinearities and the harmonic potential are discussed.
► 2D exact quantized nonlinear matter wave functions with the odd and even parities are obtained.
► The 2D ground-state matter wave with attractive two-body and repulsive three-body interactions is stable.
► Experimental realization of our results in future experiments is proposed.