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Acta Physica Sinica

Stability of dipolar soliton in crossed linear and nonlinear optical lattices

Yong Wen-Mei, Chen Hai-Jun

Published Jan 1, 2014• 1 citation
Publisher

Abstract

Stability of a dipolar Bose-Einstein condensate (BEC) soliton in crossed linear and nonlinear optical lattices is investigated using variational approximation. The Euler-Lagrange equations for variational parameters and the effective potential are derived by means of a cylindrically symmetric Gaussian ansatz, while the equilibrium widths are determined by minimization of the effective potential. In the presence of a periodic spatial variation of short-range contact interaction, the localized bound states can exist for both attractive and repulsive dipolar interactions. And the domain of stable dipolar BEC solitons is illustrated in a phase plot of the nonlinearities. Finally, we give the evolution of the variational width for different values of the nonlinearities.

DOI
10.7498/aps.63.150302

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Stability of a dipolar Bose-Einstein condensate (BEC) soliton in crossed linear and nonlinear optical lattices is investigated using variational approximation. The Euler-Lagrange equations for variational parameters and the effective potential are derived by means of a cylindrically symmetric Gaussian ansatz, while the equilibrium widths are determined by minimization of the effective potential. In the presence of a periodic spatial variation of short-range contact interaction, the localized bound states can exist for both attractive and repulsive dipolar interactions. And the domain of stable dipolar BEC solitons is illustrated in a phase plot of the nonlinearities. Finally, we give the evolution of the variational width for different values of the nonlinearities.
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By means of variational solution and direct numerical simulation of the Gross-Pitaevskii equation (GPE), we have studied the stability of matter-wave solitons in two-dimensional (2D) Bose-Einstein condensations (BECs), with 2D linear and nonlinear optical lattices (OLs). Using the static variational approach and Vakhitov-Kolokolov criterion necessary for stability, we obtain the stability condition for solitons in different combinations of OL's parameters. We show that the 2D linear and nonlinear optical lattices allow us to stabilize 2D solitons for both attractive and repulsive interactions. We also study the time-evolution problems of 2D BECs, using the time-dependent variational approach and numerical solution of GPE for 2D linear and nonlinear OLs. Very good agreement between the results corresponding to both treatments is observed.
We analyze the existence and stability of spatially extended (Bloch-type) and localized states of a Bose-Einstein condensate loaded into an optical lattice. In the framework of the Gross-Pitaevskii equation with a periodic potential, we study the band-gap structure of the matter-wave spectrum in both the linear and nonlinear regimes. We demonstrate the existence of families of spatially localized matter-wave gap solitons, and analyze their stability in different band gaps, for both repulsive and attractive atomic interactions.
Recent research works on ultra cold quantum gases demonstrated that dipolar Bose–Einstein condensates (BECs) exhibit rich spatiotemporal dynamic where both local and nonlocal interactions are considered. We explore theoretically the possibility of controlling the formation and dynamics of soliton molecules in binary dipolar condensates with spin-orbit coupling (SOC). We exploit the variational technique to derive the new equations of motion for the widths and amplitudes, the effective potential and the oscillation frequency of the molecules. Our study confirms the existence of stable localized bound states in an optical potential. We find that the integrity of the molecules is influenced by the physical parameters, notably the local and nonlocal interactions with the SOC. These parameters are carefully chosen by the Vakhitov–Kolokolov (VK) criterion to ensure the stability of the molecules. We present the results of numerical experiments and confirm the analytical predictions. Moreover, we show the soliton–soliton interaction in each molecule when the local interactions are strong.
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We predict the existence of stable fundamental and vortical bright solitons in dipolar Bose-Einstein condensates (BECs) with repulsive dipole-dipole interactions (DDI). The condensate is trapped in the 2D plane with the help of the repulsive contact interactions whose local strength grows ∼r4\sim r^{4}∼r4 from the center to periphery, while dipoles are oriented perpendicular to the self-trapping plane. The confinement in the perpendicular direction is provided by the usual harmonic-oscillator potential. The objective is to extend the recently induced concept of the self-trapping of bright solitons and solitary vortices in the pseudopotential, which is induced by the repulsive local nonlinearity with the strength growing from the center to periphery, to the case when the trapping mechanism competes with the long-range repulsive DDI. Another objective is to extend the analysis for elliptic vortices and solitons in an anisotropic nonlinear pseudopotential. Using the variational approximation (VA) and numerical simulations, we construct families of self-trapped modes with vorticities ℓ=0\ell =0ℓ=0 (fundamental solitons), ℓ=1\ell =1ℓ=1, and ℓ=2\ell =2ℓ=2. The fundamental solitons and vortices with ℓ=1\ell =1ℓ=1 exist up to respective critical values of the eccentricity of the anisotropic pseudopotential, being stable in the entire existence regions. The vortices with ℓ=2\ell =2ℓ=2 are stable solely in the isotropic model.