# Dynamics of Bose-Einstein condensates under the influence of periodic and harmonic potentials

## Abstract

A variational method is developed to describe the dynamics of a Bose-Einstein condensate (BEC) trapped in an applied external potential consisting of both a harmonic and periodic component. Using this variational method, the BEC dynamics is shown to be well approximated by four coupled nonlinear differential equations, which describe the fundamental interactions in the system arising from the interplay of amplitude (width), chirp, center position, and center frequency. The simplified analytic theory allows for an efficient and convenient method for characterizing the experimental BEC behavior when localized condensates are generated. It further gives the critical strength ratio of harmonic to periodic potential necessary to support multiple stable lattice sites for the condensate and demonstrates that there can be an underlying chaotic behavior in the condensate system.

- Authors:

- Department of Applied Mathematics, University of Washington, Seattle, Washington 98195 (United States)

- Publication Date:

- OSTI Identifier:
- 21072403

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics; Journal Volume: 75; Journal Issue: 3; Other Information: DOI: 10.1103/PhysRevE.75.036214; (c) 2007 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; AMPLITUDES; BOSE-EINSTEIN CONDENSATION; CHAOS THEORY; DIFFERENTIAL EQUATIONS; HARMONIC POTENTIAL; NONLINEAR PROBLEMS; PERIODICITY; TRAPPING; VARIATIONAL METHODS

### Citation Formats

```
Berry, N. Hawk, and Kutz, J. Nathan.
```*Dynamics of Bose-Einstein condensates under the influence of periodic and harmonic potentials*. United States: N. p., 2007.
Web. doi:10.1103/PHYSREVE.75.036214.

```
Berry, N. Hawk, & Kutz, J. Nathan.
```*Dynamics of Bose-Einstein condensates under the influence of periodic and harmonic potentials*. United States. doi:10.1103/PHYSREVE.75.036214.

```
Berry, N. Hawk, and Kutz, J. Nathan. Thu .
"Dynamics of Bose-Einstein condensates under the influence of periodic and harmonic potentials". United States.
doi:10.1103/PHYSREVE.75.036214.
```

```
@article{osti_21072403,
```

title = {Dynamics of Bose-Einstein condensates under the influence of periodic and harmonic potentials},

author = {Berry, N. Hawk and Kutz, J. Nathan},

abstractNote = {A variational method is developed to describe the dynamics of a Bose-Einstein condensate (BEC) trapped in an applied external potential consisting of both a harmonic and periodic component. Using this variational method, the BEC dynamics is shown to be well approximated by four coupled nonlinear differential equations, which describe the fundamental interactions in the system arising from the interplay of amplitude (width), chirp, center position, and center frequency. The simplified analytic theory allows for an efficient and convenient method for characterizing the experimental BEC behavior when localized condensates are generated. It further gives the critical strength ratio of harmonic to periodic potential necessary to support multiple stable lattice sites for the condensate and demonstrates that there can be an underlying chaotic behavior in the condensate system.},

doi = {10.1103/PHYSREVE.75.036214},

journal = {Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics},

number = 3,

volume = 75,

place = {United States},

year = {Thu Mar 15 00:00:00 EDT 2007},

month = {Thu Mar 15 00:00:00 EDT 2007}

}