摘要
This brief review summarizes recent theoretical and experimental results which predict and establish the existence of quantum droplets(QDs),i.e.,robust two-and three-dimensional(2D and 3D)self-trapped states in Bose-Einstein condensates(BECs),which are stabilized by effective self-repulsion induced by quantum fluctuations around the mean-field(MF)states[alias the Lee-Huang-Yang(LHY)effect].The basic models are presented,taking special care of the dimension crossover,2D→3D.Recently reported experimental results,which exhibit stable 3D and quasi-2D QDs in binary BECs,with the inter-component attraction slightly exceeding the MF self-repulsion in each component,and in single-component condensates of atoms carrying permanent magnetic moments,are presented in some detail.The summary of theoretical results is focused,chiefly,on 3D and quasi-2D QDs with embedded vorticity,as the possibility to stabilize such states is a remarkable prediction.Stable vortex states are presented both for QDs in free space,and for singular but physically relevant 2D modes pulled to the center by the inverse-square potential,with the quantum collapse suppressed by the LHY effect.
基金
Y.L.acknowledges the supports of the National Natural Science Foundation of China(Grant Nos.11874112 and 11905032)
the Key Research Projects of General Colleges in Guangdong Province through grant No.2019KZDXM001
the Foundation for Distinguished Young Talents in Higher Education of Guangdong through grant No.2018KQNCX279
The work of BAM on this topic was supported,in part,by grant No.1286/17 from the Israel Science Foundation.
