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arXiv 2006.00646cond-mat.quant-gasnlin.PS
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自旋-轨道耦合旋转自旋1凝聚体中涡格的形成

Vortex-lattice formation in a spin-orbit coupled rotating spin-1 condensate

S. K. Adhikari

摘要:

利用数值求解平均场Gross-Pitaevskii方程,研究了旋转{Rashba}自旋轨道耦合准二维(准二维)超精细自旋1旋量玻色-爱因斯坦凝聚体(BEC)在$x-y$平面内的涡旋晶格形成.这个系统的波函数有三个分量,对应于超精细自旋$F_z= +1,0,-1$的三个投影。在这种情况下,非旋转的{Rashba} SO耦合旋量BEC可以具有三个分量中不同角动量的涡旋形式的拓扑激发,例如铁磁和反铁磁旋量BEC中的$(0,+1,+2)$ -和$(-1,0,+1)$ -型状态:括号中的数字表示三个分量的涡旋状态的固有角动量,其中负号表示反涡旋。这些具有内禀涡度的状态的存在打破了沿$z$和$-z$轴的具有涡度的旋转之间的对称性,从而在旋转的准2D自旋1旋量铁磁和反铁磁BEC中产生了丰富多样的涡旋晶格和反涡旋晶格状态,这在标量BEC中是不可能的。{For在弱SO耦合下,我们发现这些态有两种对称性,$-$为六角对称和“正方形”对称。六边形(正方形)对称状态具有排列在闭合同心轨道中的涡旋,在连续轨道中具有最大值的$6, 12, 18...$($8,12,16...$)涡旋。在这两种对称性中,方涡格态的能量较小。

英文摘要:

We study the vortex-lattice formation in a rotating {Rashba} spin-orbit (SO) coupled quasi-two-dimensional (quasi-2D) hyper-fine spin-1 spinor Bose-Einstein condensate (BEC) in the $x-y$ plane using a numerical solution of the underlying mean-field Gross-Pitaevskii equation. % The wave function for this system %has three components corresponding to the three projections of hyper-fine spin $F_z= +1,0,-1$. In this case, the non-rotating {Rashba} SO-coupled spinor BEC can have topological excitation in the form of vortices of different angular momenta in the three components, e.g. the $(0,+1,+2)$- and $(-1,0,+1)$-type states in ferromagnetic and anti-ferromagnetic spinor BEC: the numbers in the parenthesis denote the intrinsic angular momentum of the vortex states of the three components with the negative sign denoting an anti-vortex. The presence of these states with intrinsic vorticity breaks the symmetry between rotation with vorticity along the $z$ and $-z$ axes and thus generates a rich variety of vortex-lattice and anti-vortex-lattice states in a rotating quasi-2D spin-1 spinor ferromagnetic and anti-ferromagnetic BEC, not possible in a scalar BEC. {For weak SO coupling, } we find two types of symmetries of these states $-$ hexagonal and "square". The hexagonal (square) symmetry state has vortices arranged in closed concentric orbits with a maximum of $6, 12, 18...$ ($8,12,16...$) vortices in successive orbits. Of these two symmetries, the square vortex-lattice state is found to have the smaller energy.

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