Singular loops and their non-Abelian geometric phases in ultracold spin-1 atoms

Presenting Author: Bharath H. M., Georgia Institute of Technology
Contributing Author(s): Matthew Boguslawski, Maryrose Barrios, Lin Xin, Michael Chapman

We use coherent control of ultracold Rubidium atoms in a dipole trap to experimentally explore the recently introduced non-Abelian geometric phases of singular loops inside the Bloch ball [1]. Non-Abelian and non-adiabatic variants of Berry's geometric phase have been pivotal in the recent advances in fault-tolerant quantum computation gates, while Berry's phase itself is at the heart of the study of topological phases of matter. In [1], geometric phase was generalized to loops on or inside the Bloch ball and was formulated as an SO(3) operator, carried by the spin-fluctuation tensor of a spin-1 system . The special class of loops inside the Bloch ball passing through the center, which we refer to as singular loops, are significant in two ways. First, their geometric phase is non-Abelian and second, their geometrical properties are qualitatively different from the nearby non-singular loops, making them akin to critical points of a quantum phase transition. [1] H. M. Bharath, “Non-Abelian geometric phases carried by the spin fluctuation tensor”, arXiv:1702.08564

Read this article online: https://arxiv.org/abs/1702.08564

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