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Chinese Physics B

Effect of interaction strength on gap solitons of Bose–Einstein condensates in optical lattices

Yang Ru-shu, Yang Jiang-he

Published Apr 1, 2008• 8 citations
Publisher

Abstract

We have developed a systematic analytical approach to the study on the dynamic properties of the linear and the nonlinear excitations for quasi-one-dimensional Bose–Einstein condensate trapped in optical lattices. A novel linear dispersion relation and an algebraic soliton solution of the condensate are derived analytically under consideration of Bose–Einstein condensate with a periodic potential. By analysing the soliton solution, we find that the interatomic interaction strength has an important effect on soliton dynamic properties of Bose–Einstein condensate.

DOI
10.1088/1674-1056/17/4/007

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We have developed a systematic analytical approach to the study on the dynamic properties of the linear and the nonlinear excitations for quasi-one-dimensional Bose–Einstein condensate trapped in optical lattices. A novel linear dispersion relation and an algebraic soliton solution of the condensate are derived analytically under consideration of Bose–Einstein condensate with a periodic potential. By analysing the soliton solution, we find that the interatomic interaction strength has an important effect on soliton dynamic properties of Bose–Einstein condensate.
We develop a systematic analytical approach to study the linear and nonlinear solitary excitations of quasi-one-dimensional Bose-Einstein condensates trapped in an optical lattice. For the linear case, the Bloch wave in the nth energy band is a linear superposition of Mathieu's functions ce_{n-1} and se_{n} ; and the Bloch wave in the nth band gap is a linear superposition of ce_{n} and se_{n} . For the nonlinear case, only solitons inside the band gaps are likely to be generated and there are two types of solitons-fundamental solitons (which is a localized and stable state) and subfundamental solitons (which is a localized but unstable state). In addition, we find that the pinning position and the amplitude of the fundamental soliton in the lattice can be controlled by adjusting both the lattice depth and spacing. Our numerical results on fundamental solitons are in quantitative agreement with those of the experimental observation [B. Eiermann, Phys. Rev. Lett. 92, 230401 (2004)]. Furthermore, we predict that a localized gap-soliton train consisting of several fundamental solitons can be realized by increasing the length of the condensate in currently experimental conditions.
By developing a multiple-scale method, we study analytically the dynamics of the soliton inside the semi-infinite band gap (SIBG) of quasi-one-dimensional Bose–Einstein condensates trapped in an optical lattice. In the linear case, a stable condition of soliton formation is obtained. For a weak nonlinearity, whether there occurs a spatially propagating or localized gap soliton is determined by the lattice depth. Meanwhile, we predict the existence of the dark (bright) gap solitons for the repulsive (attractive) interactions in the SIBG, different from that of the gap solitons in other energy gaps. And the collision of two dark (or bright) solitons is nearly elastic under a safe range of atomic numbers. An experimental protocol is further designed for observing these phenomena.
Abstract Vector gap solitons in quasi-two-dimensional Bose–Einstein condensate loaded in a square optical lattice with spin-orbit and Rabi coupling are investigated theoretically. The solitons are obtained by the Newton-Conjugate-Gradient method for various physical parameters. The stability properties of gap solitons are theoretically analyzed by direct nonlinear dynamical evolution. It is found that the existence of gap solitons is sensitive to the spin-orbit and Rabi coupling strength. Smaller Rabi coupling strength is beneficial for the excitation of solitons in the semi-infinite gap. Conversely, larger Rabi coupling strength is beneficial for the soliton excitation in the first gap. The dynamical stability of these gap solitons depends on the spin-orbit and Rabi coupling strength, and the location of the soliton in the bandgap. These findings may contribute to understanding the topological excitations in condensed matter systems.
Abstract We investigate the properties of gap solitons in spin–orbit-coupled Bose–Einstein condensates in mixed linear–nonlinear optical lattices. The mixed linear–nonlinear optical lattices can support parity-time (PT)-symmetric soliton solutions, and these PT-symmetric solitons can stably exist in the semi-infinite gap of linear optical lattices. The PT-symmetric gap-stripe solitons are found by increasing the strength of the spin–orbit coupling. It is found that the amplitude of the nonlinear optical lattices can significantly affect the stability of these gap and gap-stripe solitons. With an increase of the amplitude of the nonlinear optical lattices, the stable domains of the gap and gap-stripe solitons are shrunk. The unstable solitons can show unique evolution characteristics and the stability analyses are also confirmed by the evolution simulations.