Gauge-Invariant Phase Mapping to Intensity Lobes of Structured Light via Closed-Loop Atomic Dark States

TL;DR

This paper introduces an analytical model demonstrating how gauge-invariant loop phases in atomic systems create observable intensity patterns in structured light, enabling phase mapping and Berry phase measurement.

Contribution

It provides a novel analytical framework linking gauge-invariant phases in closed-loop atomic systems to observable optical interference patterns and Berry phase detection.

Findings

Loop phase influences Laguerre Gaussian beam intensity patterns.

Visibility depends on optical depth and interference terms.

Experimental feasibility with cold atoms or solid-state platforms.

Abstract

We present an analytical model showing how the gauge-invariant loop phase in a three-level closed-loop atomic system imprints as bright-dark lobes in Laguerre Gaussian probe beam intensity patterns. In the weak probe limit, the output intensity in such systems include Beer-Lambert absorption, a scattering term and loop phase dependent interference term with optical depth controlling visibility. These systems enable mapping of arbitrary phases via interference rotation and offer a platform to measure Berry phase. Berry phase emerge as a geometric holonomy acquired by the dark states during adiabatic traversal of LG phase defined in a toroidal parameter space. Manifesting as fringe shifts which are absent in open systems, experimental realization using cold atoms or solid state platforms appears feasible, positioning structured light in closed-loop systems as ideal testbeds for geometric phases in quantum optics.