Abstract
This mini-review collects results predicting the creation of matter-wave solitons by the spinor system of Gross-Pitaevskii equations (GPEs) with the self-attractive cubic nonlinearity and linear first-order-derivative terms accounting for the spin-orbit coupling (SOC). In 1D, the so-predicted bright solitons are similar to usual ones, supported by the GPE in the absence of SOC. Essentially new results were recently obtained for 2D and 3D systems: SOC suppresses the collapse instability in the multidimensional GPE, creating 2D ground-state solitons and metastable 3D ones of two types: semi-vortices (SVs), with vorticities m = 1 in one component and m = 0 in the other, and mixed modes (MMs), with m = 0 and present in both components. With the Galilean invariance broken by SOC, moving solitons exist up to a certain critical velocity. The latest result predicts stable 2D “quantum droplets” of the MM type in the presence of the Lee-Huang-Yang corrections to the GPE system, induced by quantum fluctuations, in the case when the inter-component attraction dominates over the self-repulsion in each component.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
