We investigate the ground states of spin-orbit coupled spin-1 Bose-Einstein condensates in the presence of Zeeman splitting.By introducing the generalized momentum operator,the linear version of the system is solved e...We investigate the ground states of spin-orbit coupled spin-1 Bose-Einstein condensates in the presence of Zeeman splitting.By introducing the generalized momentum operator,the linear version of the system is solved exactly,yielding a set of Bessel vortices.Additionally,based on linear solution and using variational approximation,the solutions for the full nonlinear system and their ground state phase diagrams are derived,including the vortex states with quantum numbers m=0,1,as well as mixed states.In this work,mixed states in spin-1 spin-orbit coupling(SOC)BEC are interpreted for the first time as weighted superpositions of three vortex states.Furthermore,the results also indicate that under strong Zeeman splitting,the system cannot form localized states.The variational solutions align well with numerical simulations,showing stable evolution and meeting the criteria for long-term observation in experiments.展开更多
基金supported by the Guangdong Basic and Applied Basic Research Foundation(Grant No.2023A1515110198)the Natural Science Foundation of Guangdong Province,China(Grant Nos.2024A1515030131 and 2021A1515010214)+2 种基金the National Natural Science Foundation of China(Grant Nos.12274077,11905032,and 12475014)the Research Fund of the Guangdong-Hong Kong-Macao Joint Laboratory for Intelligent Micro-Nano Optoelectronic Technology(Grant No.2020B1212030010)the Israel Science Foundation(Grant No.1695/22).
文摘We investigate the ground states of spin-orbit coupled spin-1 Bose-Einstein condensates in the presence of Zeeman splitting.By introducing the generalized momentum operator,the linear version of the system is solved exactly,yielding a set of Bessel vortices.Additionally,based on linear solution and using variational approximation,the solutions for the full nonlinear system and their ground state phase diagrams are derived,including the vortex states with quantum numbers m=0,1,as well as mixed states.In this work,mixed states in spin-1 spin-orbit coupling(SOC)BEC are interpreted for the first time as weighted superpositions of three vortex states.Furthermore,the results also indicate that under strong Zeeman splitting,the system cannot form localized states.The variational solutions align well with numerical simulations,showing stable evolution and meeting the criteria for long-term observation in experiments.
