Magnetic Local Field Effect In The Interaction Between Spinor Bose-einstein Condensate And Microwave

Atomic Bose-Einstein condensates(BEC)have very important implications in the fields such as precision measurements,quantum simulation,quantum information and quantum computing.It is now a hot research spot in physics.Electromagnetic wave is the most important tool for coherent controlling of BEC.When it is used to manipulate BEC,the BEC as a media will simultaneously have a feedback effect,which is the so called local field effect.Usually,it is believed that the atomic gas is so dilute,this effect is very weak and can be neglected.But some recent researches found that when considering problems like the diffraction of a BEC by standing optical waves,this effect can have a remarkable influence.The recent researches on local field effect are mainly performed in the system of single component BEC interacting with light via electric dipole transition.In the field of cold atomic physics,the spinor BEC is another important research object.The spinor BEC is usually coherently controlled by microwave via magnetic dipole transition.However,the local field effect for such interaction(called magnetic local field effect,and to distinguish from each other the local filed effect in the case of electric dipole transition will be called electric local filed effect)has not been examined yet.Here we studied it in a system of interacting spin-1/2 BEC and microwave.The equations of motion governing the system are deduced,and we find that the magnetic local field effect induces both a long range interaction and a short range contact interaction effectively.Based on the above 'mentioned theory,we firstly investigated a simple one dimensional system.Our analytical results,confirmed by the numerical simulations,show that the magnetic local field effect induced effective long range interaction leads to modulational instability and can create bright hybrid materwave-microwave solitons in the system.When strong repulsive contact interaction exists,we analytically construct the soliton solution by means of Thomas-Fermi approximation.The results show that the repulsive contact interaction will not destroy the soliton regardless of its strength.When the dimension of a system is increased,there will usually be more abundant physical phenomena.So a two dimensional system is studied afterwards.In a two dimensional BEC,stable vortexes with large topological charge are not only a subject of fundamental significance,but are also sought to be useful in the areas such as quantum simulation,processing and storage of quantum information.However,the creation of such stable large topological charged vortexes is still an unsolved problem(In conventional BEC,vortexes with topological charge larger than 1 are unstable).Here,we demonstrate that the magnetic local field effect induced effective long range interaction can create robust bright solitons and solitary vortexes(numerically checked for topological charge 5).When the strength of attractive contact interaction in the system surpasses a certain critical value,the solitons and solitary vortexes will collapse.Below this critical value,the solitons and solitary vortexes can evolve stably in the case of weak interaction,and a strong interaction will cause oscillation of soliton profile and splitting of vortex ring.The stability of vortexes is linearly related to their topological numbers,thus high-order vortexes are more robust than their low-order counterparts.In the case of strong repulsive contact interaction,the results from Thomas-Fermi approximation indicate no destroying of the solitons.Spin-orbit coupling refers to the interaction between a particle's spin freedom and its motion in space.In the cold atom regime,now an effective spin-orbit coupling can be realized in BEC by a Raman scattering scheme.We further introduce the magnetic local field effect induced.effective long range,interaction.in such a system and studied the soliton phenomenon.With both numerical and variational approaches,we found that there are three kinds(normal,stripe and plane-wave)of solitons in the system.Among them,the normal and stripe ones can evolve stably,while the plane-wave one will leave its initial positon and become a moving one as time goes.And we also found that the interaction can wipe off a quantum phase transition in the system.Our researches not only can help people getting a deeper understanding of the Spinor BEC-Microwave interacting system,but also may have potential implications.The solitons may be used to build matterwave interferometry and atom laser which are important tools in the field of precision measurements.The vortexes can be used to processing and storage quantum information.Lastly,the reaches here can also be generalized to the systems of molecular BEC or degenerate atomic Fermi gas interacting with microwave.