### Abstract

We introduce a dynamical model of a Bose-Einstein condensate based on the one-dimensional (1D) Gross-Pitaevskii equation (GPE) with a nonlinear optical lattice (NOL), which is represented by the cubic term whose coefficient is periodically modulated in the coordinate. The model describes a situation when the atomic scattering length is spatially modulated, via the optically controlled Feshbach resonance, in an optical lattice created by interference of two laser beams. Relatively narrow solitons supported by the NOL are predicted by means of the variational approximation (VA), and an averaging method is applied to broad solitons. A different feature is a minimum norm (number of atoms), N=Nmin, necessary for the existence of solitons. The VA predicts Nmin very accurately. Numerical results are chiefly presented for the NOL with the zero spatial average value of the nonlinearity coefficient. Solitons with values of the amplitude A larger than at N=Nmin are stable. Unstable solitons with smaller, but not too small, A rearrange themselves into persistent breathers. For still smaller A, the soliton slowly decays into radiation without forming a breather. Broad solitons with very small A are practically stable, as their decay is extremely slow. These broad solitons may freely move across the lattice, featuring quasielastic collisions. Narrow solitons, which are strongly pinned to the NOL, can easily form stable complexes. Finally, the weakly unstable low-amplitude solitons are stabilized if a cubic term with a constant coefficient, corresponding to weak attraction, is included in the GPE.

Original language | English |
---|---|

Article number | 046610 |

Journal | Physical Review E - Statistical, Nonlinear, and Soft Matter Physics |

Volume | 72 |

Issue number | 4 |

DOIs | |

Publication status | Published - Oct 1 2005 |

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### All Science Journal Classification (ASJC) codes

- Statistical and Nonlinear Physics
- Statistics and Probability
- Condensed Matter Physics

### Cite this

*Physical Review E - Statistical, Nonlinear, and Soft Matter Physics*,

*72*(4), [046610]. https://doi.org/10.1103/PhysRevE.72.046610

**Matter-wave solitons in nonlinear optical lattices.** / Sakaguchi, Hidetsugu; Malomed, Boris A.

Research output: Contribution to journal › Article

*Physical Review E - Statistical, Nonlinear, and Soft Matter Physics*, vol. 72, no. 4, 046610. https://doi.org/10.1103/PhysRevE.72.046610

}

TY - JOUR

T1 - Matter-wave solitons in nonlinear optical lattices

AU - Sakaguchi, Hidetsugu

AU - Malomed, Boris A.

PY - 2005/10/1

Y1 - 2005/10/1

N2 - We introduce a dynamical model of a Bose-Einstein condensate based on the one-dimensional (1D) Gross-Pitaevskii equation (GPE) with a nonlinear optical lattice (NOL), which is represented by the cubic term whose coefficient is periodically modulated in the coordinate. The model describes a situation when the atomic scattering length is spatially modulated, via the optically controlled Feshbach resonance, in an optical lattice created by interference of two laser beams. Relatively narrow solitons supported by the NOL are predicted by means of the variational approximation (VA), and an averaging method is applied to broad solitons. A different feature is a minimum norm (number of atoms), N=Nmin, necessary for the existence of solitons. The VA predicts Nmin very accurately. Numerical results are chiefly presented for the NOL with the zero spatial average value of the nonlinearity coefficient. Solitons with values of the amplitude A larger than at N=Nmin are stable. Unstable solitons with smaller, but not too small, A rearrange themselves into persistent breathers. For still smaller A, the soliton slowly decays into radiation without forming a breather. Broad solitons with very small A are practically stable, as their decay is extremely slow. These broad solitons may freely move across the lattice, featuring quasielastic collisions. Narrow solitons, which are strongly pinned to the NOL, can easily form stable complexes. Finally, the weakly unstable low-amplitude solitons are stabilized if a cubic term with a constant coefficient, corresponding to weak attraction, is included in the GPE.

AB - We introduce a dynamical model of a Bose-Einstein condensate based on the one-dimensional (1D) Gross-Pitaevskii equation (GPE) with a nonlinear optical lattice (NOL), which is represented by the cubic term whose coefficient is periodically modulated in the coordinate. The model describes a situation when the atomic scattering length is spatially modulated, via the optically controlled Feshbach resonance, in an optical lattice created by interference of two laser beams. Relatively narrow solitons supported by the NOL are predicted by means of the variational approximation (VA), and an averaging method is applied to broad solitons. A different feature is a minimum norm (number of atoms), N=Nmin, necessary for the existence of solitons. The VA predicts Nmin very accurately. Numerical results are chiefly presented for the NOL with the zero spatial average value of the nonlinearity coefficient. Solitons with values of the amplitude A larger than at N=Nmin are stable. Unstable solitons with smaller, but not too small, A rearrange themselves into persistent breathers. For still smaller A, the soliton slowly decays into radiation without forming a breather. Broad solitons with very small A are practically stable, as their decay is extremely slow. These broad solitons may freely move across the lattice, featuring quasielastic collisions. Narrow solitons, which are strongly pinned to the NOL, can easily form stable complexes. Finally, the weakly unstable low-amplitude solitons are stabilized if a cubic term with a constant coefficient, corresponding to weak attraction, is included in the GPE.

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U2 - 10.1103/PhysRevE.72.046610

DO - 10.1103/PhysRevE.72.046610

M3 - Article

AN - SCOPUS:28844491730

VL - 72

JO - Physical Review E

JF - Physical Review E

SN - 2470-0045

IS - 4

M1 - 046610

ER -