Non-Abelian adiabatic geometric transformations in a cold strontium gas

F Leroux,K Pandey,C Miniatura,B Grémaud,R Rehbi,D Wilkowski,F Chevy

doi:10.1038/s41467-018-05865-3

Abstract

Topology, geometry, and gauge fields play key roles in quantum physics as exemplified by fundamental phenomena such as the Aharonov–Bohm effect, the integer quantum Hall effect, the spin Hall, and topological insulators. The concept of topological protection has also become a salient ingredient in many schemes for quantum information processing and fault-tolerant quantum computation. The physical properties of such systems crucially depend on the symmetry group of the underlying holonomy. Here, we study a laser-cooled gas of strontium atoms coupled to laser fields through a four-level resonant tripod scheme. By cycling the relative phases of the tripod beams, we realize non-Abelian SU(2) geometrical transformations acting on the dark states of the system and demonstrate their non-Abelian character. We also reveal how the gauge field imprinted on the atoms impact their internal state dynamics. It leads to a thermometry method based on the interferometric displacement of atoms in the tripod beams.

Highlights

Topology, geometry, and gauge fields play key roles in quantum physics as exemplified by fundamental phenomena such as the Aharonov–Bohm effect, the integer quantum Hall effect, the spin Hall, and topological insulators
If non-adiabatic manipulations are promising methods for quantum computing, they prevent the study of external dynamic of quantum system in a non-Abelian gauge field, where non-trivial coupling occurs between the internal qubit state dynamics and the center-of-mass motion of the particle
We report on non-Abelian adiabatic geometric transformations implemented on a non-interacting cold fermionic gas of strontium-87 atoms by using a four-level resonant tripod scheme set on the 1S0; Fg 1⁄4 9=2 ! 3 P1; Fe 1⁄4 9=2 intercombination line at λ = 689 nm

Summary

Introduction

Geometry, and gauge fields play key roles in quantum physics as exemplified by fundamental phenomena such as the Aharonov–Bohm effect, the integer quantum Hall effect, the spin Hall, and topological insulators. In 1984, Berry published the remarkable discovery that cyclic parallel transport of quantum states causes the appearance of geometrical phase factors[1] His discovery, along with precursor works[2,3], unified seemingly different phenomena within the framework of gauge theories[4,5]. This seminal work was rapidly generalized to non-adiabatic and noncyclic evolutions[5] and, most saliently for our concern here, to degenerate states by Wilczek and Zee[6] In this case, the underlying symmetry of the degenerate subspace leads to a non-Abelian gauge field structure. These three coplanar coupling laser beams are set on resonance with their common excited state jei 1⁄4 jFe 1⁄4 9=2; me 1⁄4 7=2i

Methods

Results

Conclusion