### Abstract

In this work, we study two-dimensional Bose-Einstein condensates confined by both a cylindrically symmetric harmonic potential and an optical lattice with equal periodicity in two orthogonal directions. We first identify the spectrum of the underlying two-dimensional linear problem through multiple-scale techniques. Then, we use the results obtained in the linear limit as a starting point for the existence and stability analysis of the lowest energy states, emanating from the linear ones, in the nonlinear problem. Two-parameter continuations of these states are performed for increasing nonlinearity and optical lattice strengths, and their instabilities and temporal evolution are investigated. It is found that the ground state as well as some of the excited states may be stable or weakly unstable for both attractive and repulsive interatomic interactions. Higher excited states are typically found to be increasingly more unstable.

Original language | English (US) |
---|---|

Article number | 195303 |

Journal | Journal of Physics B: Atomic, Molecular and Optical Physics |

Volume | 41 |

Issue number | 19 |

DOIs | |

State | Published - Oct 14 2008 |

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### ASJC Scopus subject areas

- Condensed Matter Physics
- Atomic and Molecular Physics, and Optics

### Cite this

*Journal of Physics B: Atomic, Molecular and Optical Physics*,

*41*(19), [195303]. https://doi.org/10.1088/0953-4075/41/19/195303

**Structure and stability of two-dimensional Bose-Einstein condensates under both harmonic and lattice confinement.** / Law, K. J H; Kevrekidis, P. G.; Anderson, Brian P; Carretero-González, R.; Frantzeskakis, D. J.

Research output: Contribution to journal › Article

*Journal of Physics B: Atomic, Molecular and Optical Physics*, vol. 41, no. 19, 195303. https://doi.org/10.1088/0953-4075/41/19/195303

}

TY - JOUR

T1 - Structure and stability of two-dimensional Bose-Einstein condensates under both harmonic and lattice confinement

AU - Law, K. J H

AU - Kevrekidis, P. G.

AU - Anderson, Brian P

AU - Carretero-González, R.

AU - Frantzeskakis, D. J.

PY - 2008/10/14

Y1 - 2008/10/14

N2 - In this work, we study two-dimensional Bose-Einstein condensates confined by both a cylindrically symmetric harmonic potential and an optical lattice with equal periodicity in two orthogonal directions. We first identify the spectrum of the underlying two-dimensional linear problem through multiple-scale techniques. Then, we use the results obtained in the linear limit as a starting point for the existence and stability analysis of the lowest energy states, emanating from the linear ones, in the nonlinear problem. Two-parameter continuations of these states are performed for increasing nonlinearity and optical lattice strengths, and their instabilities and temporal evolution are investigated. It is found that the ground state as well as some of the excited states may be stable or weakly unstable for both attractive and repulsive interatomic interactions. Higher excited states are typically found to be increasingly more unstable.

AB - In this work, we study two-dimensional Bose-Einstein condensates confined by both a cylindrically symmetric harmonic potential and an optical lattice with equal periodicity in two orthogonal directions. We first identify the spectrum of the underlying two-dimensional linear problem through multiple-scale techniques. Then, we use the results obtained in the linear limit as a starting point for the existence and stability analysis of the lowest energy states, emanating from the linear ones, in the nonlinear problem. Two-parameter continuations of these states are performed for increasing nonlinearity and optical lattice strengths, and their instabilities and temporal evolution are investigated. It is found that the ground state as well as some of the excited states may be stable or weakly unstable for both attractive and repulsive interatomic interactions. Higher excited states are typically found to be increasingly more unstable.

UR - http://www.scopus.com/inward/record.url?scp=54749130714&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=54749130714&partnerID=8YFLogxK

U2 - 10.1088/0953-4075/41/19/195303

DO - 10.1088/0953-4075/41/19/195303

M3 - Article

AN - SCOPUS:54749130714

VL - 41

JO - Journal of Physics B: Atomic, Molecular and Optical Physics

JF - Journal of Physics B: Atomic, Molecular and Optical Physics

SN - 0953-4075

IS - 19

M1 - 195303

ER -