# Topological objects in two-component Bose-Einstein condensates

## Abstract

We study the topological objects in two-component Bose-Einstein condensates. We compare two competing theories of two-component Bose-Einstein condensates, the popular Gross-Pitaevskii theory, and the recently proposed gauge theory of two-component Bose-Einstein condensate which has an induced vorticity interaction. We show that two theories produce very similar topological objects, in spite of the obvious differences in dynamics. Furthermore we show that the gauge theory of two-component Bose-Einstein condensates, with the U(1) gauge symmetry, is remarkably similar to the Skyrme theory. Just like the Skyrme theory this theory admits the non-Abelian vortex, the helical vortex, and the vorticity knot. We construct the lightest knot solution in two-component Bose-Einstein condensates numerically, and discuss how the knot can be constructed in the spin-(1/2) condensate of {sup 87}Rb atoms.

- Authors:

- Center for Theoretical Physics, College of Natural Sciences, Seoul National University, Seoul 151-742 (Korea, Republic of) and C. N. Yang Institute for Theoretical Physics, State University of New York, Stony Brook, New York 11790 (United States)
- (Korea, Republic of)

- Publication Date:

- OSTI Identifier:
- 20786340

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Physical Review. A; Journal Volume: 72; Journal Issue: 6; Other Information: DOI: 10.1103/PhysRevA.72.063603; (c) 2005 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 74 ATOMIC AND MOLECULAR PHYSICS; 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; ATOMS; BOSE-EINSTEIN CONDENSATION; COMPARATIVE EVALUATIONS; GAUGE INVARIANCE; RUBIDIUM 87; SKYRME POTENTIAL; SPIN; TOPOLOGY; U-1 GROUPS; VORTICES

### Citation Formats

```
Cho, Y. M., Khim, Hyojoong, Zhang, Pengming, and School of Physics, College of Natural Sciences, Seoul National University, Seoul 151-742.
```*Topological objects in two-component Bose-Einstein condensates*. United States: N. p., 2005.
Web. doi:10.1103/PHYSREVA.72.0.

```
Cho, Y. M., Khim, Hyojoong, Zhang, Pengming, & School of Physics, College of Natural Sciences, Seoul National University, Seoul 151-742.
```*Topological objects in two-component Bose-Einstein condensates*. United States. doi:10.1103/PHYSREVA.72.0.

```
Cho, Y. M., Khim, Hyojoong, Zhang, Pengming, and School of Physics, College of Natural Sciences, Seoul National University, Seoul 151-742. Thu .
"Topological objects in two-component Bose-Einstein condensates". United States.
doi:10.1103/PHYSREVA.72.0.
```

```
@article{osti_20786340,
```

title = {Topological objects in two-component Bose-Einstein condensates},

author = {Cho, Y. M. and Khim, Hyojoong and Zhang, Pengming and School of Physics, College of Natural Sciences, Seoul National University, Seoul 151-742},

abstractNote = {We study the topological objects in two-component Bose-Einstein condensates. We compare two competing theories of two-component Bose-Einstein condensates, the popular Gross-Pitaevskii theory, and the recently proposed gauge theory of two-component Bose-Einstein condensate which has an induced vorticity interaction. We show that two theories produce very similar topological objects, in spite of the obvious differences in dynamics. Furthermore we show that the gauge theory of two-component Bose-Einstein condensates, with the U(1) gauge symmetry, is remarkably similar to the Skyrme theory. Just like the Skyrme theory this theory admits the non-Abelian vortex, the helical vortex, and the vorticity knot. We construct the lightest knot solution in two-component Bose-Einstein condensates numerically, and discuss how the knot can be constructed in the spin-(1/2) condensate of {sup 87}Rb atoms.},

doi = {10.1103/PHYSREVA.72.0},

journal = {Physical Review. A},

number = 6,

volume = 72,

place = {United States},

year = {Thu Dec 15 00:00:00 EST 2005},

month = {Thu Dec 15 00:00:00 EST 2005}

}