Non-Abelian adiabatic geometric transformations in a cold Strontium gas

TL;DR

This paper demonstrates non-Abelian SU(2) geometric transformations in a cold Strontium gas using laser-induced tripod schemes, revealing their non-Abelian nature and introducing a new thermometry method based on gauge field effects.

Contribution

It experimentally realizes and characterizes non-Abelian geometric transformations in a cold atomic gas, advancing quantum simulation and control techniques.

Findings

Successful implementation of non-Abelian SU(2) transformations

Observation of gauge field effects on atomic state dynamics

Development of a new thermometry method based on interferometry

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. We study here a laser-cooled gas of strontium atoms coupled to laser fields through a 4-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 new thermometry method based on the interferometric displacement of atoms in the tripod beams.