Two-dimensional solitons and quantum droplets supported by competing self- and cross-interactions in spin-orbit-coupled condensates

Abstract

We study two-dimensional (2D) matter-wave solitons in spinor Bose-Einstein\ncondensates (BECs) under the action of the spin-orbit coupling (SOC) and\nopposite signs of the self- and cross-interactions. Stable 2D two-component\nsolitons of the mixed-mode (MM) type are found if the cross-interaction between\nthe components is attractive, while the self-interaction is repulsive in each\ncomponent. Stable solitons of the semi-vortex type are formed in the opposite\ncase, under the action of competing self-attraction and cross-repulsion. The\nsolitons exist with the total norm taking values below a collapse threshold.\nFurther, in the case of the repulsive self-interaction and inter-component\nattraction, stable 2D self-trapped modes, which may be considered as quantum\ndroplets (QDs), are created if the beyond-mean-field Lee-Huang-Yang (LHY) terms\nare added to the self-repulsion in the underlying system of coupled\nGross-Pitaevskii equations. Stable QDs of the MM type, of a large size with an\nanisotropic density profile, exist with arbitrarily large values of the norm,\nas the LHY terms eliminate the collapse. The effect of the SOC term on\ncharacteristics of the QDs is systematically studied. We also address the\nexistence and stability of QDs in the case of SOC with mixed Rashba and\nDresselhaus terms, which makes the density profile of the QD more isotropic.\nThus, QDs in the spin-orbit-coupled binary BEC are for the first time studied\nin the present work.\n