### Abstract

We present a many-body theory of nonlinear atom optics, and discuss some of its physical implications in the coherent regime. Considering a system of N identical two-level atoms interacting with classical and quantum-mechanical electromagnetic fields, we derive a Fock-space many-particle master equation. Introducting a Bogoliubov-Born-Green-Kirkwood-Yvon hierarchy and a Hartree-Fock factorization to truncate this hierarchy, we obtain an effective nonlinear single-particle master equation that forms the basis of nonlinear atom optics. In the second part of the paper, we concentrate on the coherent part of that master equation, and derive an effective single-atom nonlinear Schrödinger equation. This equation leads to the prediction of a number of effects, and, in particular, several kinds of atomic solitons. We discuss and numerically study two such kinds of solitons, Thirring solitons and gap solitons. Finally, the axial containment of an atomic gap soliton is illustrated.

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

Pages (from-to) | 1681-1691 |

Number of pages | 11 |

Journal | Physical Review A |

Volume | 50 |

Issue number | 2 |

DOIs | |

State | Published - 1994 |

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### ASJC Scopus subject areas

- Physics and Astronomy(all)
- Atomic and Molecular Physics, and Optics

### Cite this

*Physical Review A*,

*50*(2), 1681-1691. https://doi.org/10.1103/PhysRevA.50.1681

**Nonlinear atom optics : General formalism and atomic solitons.** / Lenz, G.; Meystre, Pierre; Wright, Ewan M.

Research output: Contribution to journal › Article

*Physical Review A*, vol. 50, no. 2, pp. 1681-1691. https://doi.org/10.1103/PhysRevA.50.1681

}

TY - JOUR

T1 - Nonlinear atom optics

T2 - General formalism and atomic solitons

AU - Lenz, G.

AU - Meystre, Pierre

AU - Wright, Ewan M

PY - 1994

Y1 - 1994

N2 - We present a many-body theory of nonlinear atom optics, and discuss some of its physical implications in the coherent regime. Considering a system of N identical two-level atoms interacting with classical and quantum-mechanical electromagnetic fields, we derive a Fock-space many-particle master equation. Introducting a Bogoliubov-Born-Green-Kirkwood-Yvon hierarchy and a Hartree-Fock factorization to truncate this hierarchy, we obtain an effective nonlinear single-particle master equation that forms the basis of nonlinear atom optics. In the second part of the paper, we concentrate on the coherent part of that master equation, and derive an effective single-atom nonlinear Schrödinger equation. This equation leads to the prediction of a number of effects, and, in particular, several kinds of atomic solitons. We discuss and numerically study two such kinds of solitons, Thirring solitons and gap solitons. Finally, the axial containment of an atomic gap soliton is illustrated.

AB - We present a many-body theory of nonlinear atom optics, and discuss some of its physical implications in the coherent regime. Considering a system of N identical two-level atoms interacting with classical and quantum-mechanical electromagnetic fields, we derive a Fock-space many-particle master equation. Introducting a Bogoliubov-Born-Green-Kirkwood-Yvon hierarchy and a Hartree-Fock factorization to truncate this hierarchy, we obtain an effective nonlinear single-particle master equation that forms the basis of nonlinear atom optics. In the second part of the paper, we concentrate on the coherent part of that master equation, and derive an effective single-atom nonlinear Schrödinger equation. This equation leads to the prediction of a number of effects, and, in particular, several kinds of atomic solitons. We discuss and numerically study two such kinds of solitons, Thirring solitons and gap solitons. Finally, the axial containment of an atomic gap soliton is illustrated.

UR - http://www.scopus.com/inward/record.url?scp=0028481785&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0028481785&partnerID=8YFLogxK

U2 - 10.1103/PhysRevA.50.1681

DO - 10.1103/PhysRevA.50.1681

M3 - Article

AN - SCOPUS:0028481785

VL - 50

SP - 1681

EP - 1691

JO - Physical Review A

JF - Physical Review A

SN - 2469-9926

IS - 2

ER -