# Rapidly rotating Bose-Einstein condensates in strongly anharmonic traps

## Abstract

We study a rotating Bose-Einstein condensate in a strongly anharmonic trap (flat trap with a finite radius) in the framework of two-dimensional Gross-Pitaevskii theory. We write the coupling constant for the interactions between the gas atoms as 1/{epsilon}{sup 2} and we are interested in the limit {epsilon}{yields}0 (Thomas-Fermi limit) with the angular velocity {omega} depending on {epsilon}. We derive rigorously the leading asymptotics of the ground state energy and the density profile when {omega} tends to infinity as a power of 1/{epsilon}. If {omega}({epsilon})={omega}{sub 0}/{epsilon} a ''hole'' (i.e., a region where the density becomes exponentially small as 1/{epsilon}{yields}{infinity}) develops for {omega}{sub 0} above a certain critical value. If {omega}({epsilon})>>1/{epsilon} the hole essentially exhausts the container and a ''giant vortex'' develops with the density concentrated in a thin layer at the boundary. While we do not analyze the detailed vortex structure we prove that rotational symmetry is broken in the ground state for const vertical bar log {epsilon} vertical bar <{omega}({epsilon}) < or approx. const/{epsilon}.

- Authors:

- Erwin Schroedinger Institute for Mathematical Physics, Boltzmanngasse 9, 1090 Vienna (Austria)
- (Austria)
- (Austria) and Fakultaet fuer Physik, Universitaet Wien, Boltzmanngasse 5, 1090 Vienna (Austria)

- Publication Date:

- OSTI Identifier:
- 20929681

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Journal of Mathematical Physics; Journal Volume: 48; Journal Issue: 4; Other Information: DOI: 10.1063/1.2712421; (c) 2007 American Institute of Physics; Country of input: International Atomic Energy Agency (IAEA)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; ANGULAR VELOCITY; BOSE-EINSTEIN CONDENSATION; BOUNDARY-VALUE PROBLEMS; COUPLING CONSTANTS; GROUND STATES; SYMMETRY BREAKING; THIN FILMS; THOMAS-FERMI MODEL; TRAPS; TWO-DIMENSIONAL CALCULATIONS

### Citation Formats

```
Correggi, M., Rindler-Daller, T., Yngvason, J., Fakultaet fuer Physik, Universitaet Wien, Boltzmanngasse 5, 1090 Vienna, and Erwin Schroedinger Institute for Mathematical Physics, Boltzmanngasse 9, 1090 Vienna.
```*Rapidly rotating Bose-Einstein condensates in strongly anharmonic traps*. United States: N. p., 2007.
Web. doi:10.1063/1.2712421.

```
Correggi, M., Rindler-Daller, T., Yngvason, J., Fakultaet fuer Physik, Universitaet Wien, Boltzmanngasse 5, 1090 Vienna, & Erwin Schroedinger Institute for Mathematical Physics, Boltzmanngasse 9, 1090 Vienna.
```*Rapidly rotating Bose-Einstein condensates in strongly anharmonic traps*. United States. doi:10.1063/1.2712421.

```
Correggi, M., Rindler-Daller, T., Yngvason, J., Fakultaet fuer Physik, Universitaet Wien, Boltzmanngasse 5, 1090 Vienna, and Erwin Schroedinger Institute for Mathematical Physics, Boltzmanngasse 9, 1090 Vienna. Sun .
"Rapidly rotating Bose-Einstein condensates in strongly anharmonic traps". United States.
doi:10.1063/1.2712421.
```

```
@article{osti_20929681,
```

title = {Rapidly rotating Bose-Einstein condensates in strongly anharmonic traps},

author = {Correggi, M. and Rindler-Daller, T. and Yngvason, J. and Fakultaet fuer Physik, Universitaet Wien, Boltzmanngasse 5, 1090 Vienna and Erwin Schroedinger Institute for Mathematical Physics, Boltzmanngasse 9, 1090 Vienna},

abstractNote = {We study a rotating Bose-Einstein condensate in a strongly anharmonic trap (flat trap with a finite radius) in the framework of two-dimensional Gross-Pitaevskii theory. We write the coupling constant for the interactions between the gas atoms as 1/{epsilon}{sup 2} and we are interested in the limit {epsilon}{yields}0 (Thomas-Fermi limit) with the angular velocity {omega} depending on {epsilon}. We derive rigorously the leading asymptotics of the ground state energy and the density profile when {omega} tends to infinity as a power of 1/{epsilon}. If {omega}({epsilon})={omega}{sub 0}/{epsilon} a ''hole'' (i.e., a region where the density becomes exponentially small as 1/{epsilon}{yields}{infinity}) develops for {omega}{sub 0} above a certain critical value. If {omega}({epsilon})>>1/{epsilon} the hole essentially exhausts the container and a ''giant vortex'' develops with the density concentrated in a thin layer at the boundary. While we do not analyze the detailed vortex structure we prove that rotational symmetry is broken in the ground state for const vertical bar log {epsilon} vertical bar <{omega}({epsilon}) < or approx. const/{epsilon}.},

doi = {10.1063/1.2712421},

journal = {Journal of Mathematical Physics},

number = 4,

volume = 48,

place = {United States},

year = {Sun Apr 15 00:00:00 EDT 2007},

month = {Sun Apr 15 00:00:00 EDT 2007}

}