# Detecting non-Abelian geometric phases with three-level {Lambda} systems

## Abstract

We show that a non-Abelian gauge potential in two nearly degenerated dressed states may be induced by two laser beams interacting with a three-level {Lambda} atomic system. We demonstrate that the populations of the atomic states at the end of a composed path formed by two closed loops are dependent on the order of those two loops, showing an unambiguous signature of the non-Abelian geometric phase. Through numerical calculations, we show that the non-Abelian feature of the geometric phases can be tested under realistic conditions.

- Authors:

- Laboratory of Quantum Information Technology, School of Physics and Telecommunication Engineering, South China Normal University, Guangzhou 510006 (China)

- Publication Date:

- OSTI Identifier:
- 22072222

- Resource Type:
- Journal Article

- Journal Name:
- Physical Review. A

- Additional Journal Information:
- Journal Volume: 84; Journal Issue: 3; Other Information: (c) 2011 American Institute of Physics; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 1050-2947

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; 74 ATOMIC AND MOLECULAR PHYSICS; GEOMETRY; LASERS; PHOTON BEAMS; POPULATION INVERSION; POTENTIALS

### Citation Formats

```
Du Yanxiong, Xue Zhengyuan, Zhang Xinding, and Yan Hui.
```*Detecting non-Abelian geometric phases with three-level {Lambda} systems*. United States: N. p., 2011.
Web. doi:10.1103/PHYSREVA.84.034103.

```
Du Yanxiong, Xue Zhengyuan, Zhang Xinding, & Yan Hui.
```*Detecting non-Abelian geometric phases with three-level {Lambda} systems*. United States. doi:10.1103/PHYSREVA.84.034103.

```
Du Yanxiong, Xue Zhengyuan, Zhang Xinding, and Yan Hui. Thu .
"Detecting non-Abelian geometric phases with three-level {Lambda} systems". United States. doi:10.1103/PHYSREVA.84.034103.
```

```
@article{osti_22072222,
```

title = {Detecting non-Abelian geometric phases with three-level {Lambda} systems},

author = {Du Yanxiong and Xue Zhengyuan and Zhang Xinding and Yan Hui},

abstractNote = {We show that a non-Abelian gauge potential in two nearly degenerated dressed states may be induced by two laser beams interacting with a three-level {Lambda} atomic system. We demonstrate that the populations of the atomic states at the end of a composed path formed by two closed loops are dependent on the order of those two loops, showing an unambiguous signature of the non-Abelian geometric phase. Through numerical calculations, we show that the non-Abelian feature of the geometric phases can be tested under realistic conditions.},

doi = {10.1103/PHYSREVA.84.034103},

journal = {Physical Review. A},

issn = {1050-2947},

number = 3,

volume = 84,

place = {United States},

year = {2011},

month = {9}

}

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