Gap-type dark localized modes in a Bose–Einstein condensate with optical lattices

Liangwei Zeng; Jianhua Zeng

doi:doi:10.1117/1.AP.1.4.046004

Advanced Photonics, 2019, 1 (4): 046004, Published Online: Aug. 28, 2019

Gap-type dark localized modes in a Bose–Einstein condensate with optical lattices Download： 589次

Liangwei Zeng ^1,2Jianhua Zeng ^1,2,*

Author Affiliations

¹ Chinese Academy of Sciences, Xi’an Institute of Optics and Precision Mechanics, State Key Laboratory of Transient Optics and Photonics, Xi’an, China

² University of Chinese Academy of Sciences, Beijing, China

Figures & Tables

Fig. 1. (a) Number of atoms (N) and (b) maximal real part of eigenvalues versus chemical potential $μ$ for 1-D matter–wave dark gap solitons found in the model with a 1-D periodic optical potential (optical lattice). The gray areas in this and other figures are the bands of linear spectra. Profiles of 1-D dark gap solitons for three marked circles in panel (b): in first BG with (c) $μ = 1.23$ and (d) $μ = 1.8$ , and in second BG with (e) $μ = 3.6$ . Here and in Fig. 2, we set $V_{0} = 3$ , and we set $g = 1.5$ throughout the paper. SIG in panel (a) [and in Figs. 2(a) and 4(a)] denotes the semi-infinite gap. Black dashed line in panel (e) represents the scaled shape of the optical lattice.

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Fig. 2. The same as in Fig. 1 but for families of 1-D matter–wave dark gap soliton clusters (composed of seven individuals), with which the nonlinear Bloch waves are accompanied. In the bottom panels (c)–(e), the spacing (Δ) between adjacent solitons is Δ $= 2 π$ , doubling the period of the optical lattice. The chemical potential $μ = 1.2$ for panel (c); its values for panels (d) and (e) are the same as those in Figs. 1(d) and 1(e), respectively.

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Fig. 3. Calculated 2-D profiles of the optical periodic potentials ( $V_{OL}$ , first row) and their contour plots (central row) as well as the corresponding linear spectra (bottom row): (a) perfect optical lattice, optical lattices with (b) single and (c) multiple bright defects (with the number of defects $n = 36$ ). Here and below, $V_{0} = 2.5$ and $V_{0} = 10$ are used, respectively, for optical lattices without and with defects. Perpendicular dashed lines in the central two panels represent two coordinates ( $x$ and $y$ ), with the intersection corresponding to origin of coordinates, point (0, 0).

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Fig. 4. Number of atoms (N) versus chemical potential $μ$ for 2-D matter–wave dark localized modes: (a) dark gap solitons with 1 defect and (b) dark gap soliton clusters supported by the 2-D periodic optical potential (optical lattice) with 36 defects. The three-dimensional density distributions, contour plots, and profiles for the marked realizations C1, C2, and D1 are shown in Figs. 5(a)–5(c), respectively.

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Fig. 5. Calculated atom density distributions (first row), their contour plots (central row), and the profiles (bottom row) of 2-D matter–wave dark gap modes: dark solitons in (a) the first BG with $μ = 3.1$ and (b) the second BG with $μ = 4.36$ ; (c) dark gap wave (soliton clusters) in the first BG with $μ = 3.1$ . Dashed lines in the first central panel represent the Cartesian co-ordinate system.

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Fig. 6. Contour plots of the atom density distribution (top), phases (central), and eigenvalues (bottom) of the 2-D matter–wave dark gap modes with engraved vortex: with vortex charge (a) $m = 1$ at $μ = 4.36$ , (b) $m = 2$ at $μ = 2.4$ , and (c) $m = 3$ at $μ = 3.1$ . Panel (a) represents dark gap vortex; panels (b) and (c) represent stable and unstable vortex states of dark gap soliton clusters, respectively.

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Liangwei Zeng, Jianhua Zeng. Gap-type dark localized modes in a Bose–Einstein condensate with optical lattices[J]. Advanced Photonics, 2019, 1(4): 046004.

Gap-type dark localized modes in a Bose–Einstein condensate with optical lattices Download： 589次

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