School of Physics, Georgia Institute of Technology, 837 State Street NW, Atlanta, Georgia 30332, USA.
Fakultät für Physik, Ludwig-Maximilians-Univesität München, 4 Schellingstraße, 80799 München, Germany.
Phys Rev Lett. 2019 Oct 25;123(17):173202. doi: 10.1103/PhysRevLett.123.173202.
The spin vector of a spin-1 system, unlike that of a spin-1/2 system, can lie anywhere on or inside the Bloch sphere representing the phase space. As a consequence, the geometrical and topological properties of the spin-1 phase space of quantum states are richer and require a generalization of Berry's phase. For special trajectories passing through the center of the Bloch sphere (singular loops), the geometric phase has a non-Abelian nature. Here, we experimentally explore this geometric phase for singular loops in a spin-1 quantum system using ultracold ^{87}Rb atoms confined in an optical trap using microwave and rf control fields.
自旋-1 系统的自旋向量与自旋-1/2 系统的自旋向量不同，它可以位于或位于代表相空间的布洛赫球上的任何位置。因此，量子态的自旋-1 相空间的几何和拓扑性质更加丰富，需要推广贝里相位。对于穿过布洛赫球中心的特殊轨迹（奇异环），几何相位具有非阿贝尔性质。在这里，我们使用微波和射频控制场在光学阱中囚禁的超冷 87Rb 原子实验性地研究了自旋-1 量子系统中奇异环的这种几何相位。
