Two-dimensional discrete solitons in rotating lattices

Abstract

We introduce a two-dimensional (2D) discrete nonlinear Schrödinger (DNLS) equation with self-attractive cubic nonlinearity in a rotating reference frame. The model applies to a Bose-Einstein condensate stirred by a rotating strong optical lattice, or light propagation in a twisted bundle of nonlinear fibers. Two species of localized states are constructed: off-axis fundamental solitons (FSs), placed at distance $R$ from the rotation pivot, and on-axis (R=0) vortex solitons (VSs), with vorticities and 2. At a fixed value of rotation frequency $\Omega$, a stability interval for the FSs is found in terms of the lattice coupling constant $C$, , with monotonically decreasing $C_{\mathrm{cr}}(R)$. VSs with S=1 have a stability interval, $\tilde{C}_{\mathrm{cr}%}^{(S=1)}(Ω)<C<C_{\mathrm{cr}}^{(S=1)}(Ω)$, which exists for below a certain critical value, ${\Omega }_{\mathrm{cr}}^{(S=1)}$. This implies that the VSs with S=1 are \emph{destabilized} in the weak-coupling limit by the rotation. On the contrary, VSs with S=2, that are known to be unstable in the standard DNLS equation, with $\Omega =0$, are \emph{stabilized} by the rotation in region $0<C<C_{\mathrm{cr}}^{(S=2)}$%, with $C_{\mathrm{cr}}^{(S=2)}$ growing as a function of $\Omega$. Quadrupole and octupole on-axis solitons are considered too, their stability regions being weakly affected by $\Omega \ne 0$.

To be published in Physical Review E

References in corpus (7)

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• Observation of Vortex Pinning in Bose-Einstein Condensates
• Observation of two-dimensional surface solitons in anisotropic waveguide arrays
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• Guiding-center solitons in rotating potentials
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Cited by in corpus (2)

• Bright solitary waves of atomic Bose-Einstein condensates under rotation
• Soliton shape and mobility control in optical lattices