Three-dimensional solitons in cross-combined linear and nonlinear optical lattices

Abstract

The existence and stability of three-dimensional (3D) solitons, in cross-combined linear and nonlinear optical lattices, are investigated. In particular, with a starting optical lattice (OL) configuration such that it is linear in the x-direction and nonlinear in the y-direction, we consider the z-direction either unconstrained (quasi-2D OL case) or with another linear OL (full 3D case). We perform this study both analytically and numerically: analytically by a variational approach based on a Gaussian ansatz for the soliton wavefunction and numerically by relaxation methods and direct integrations of the corresponding Gross-Pitaevskii equation. We conclude that, while 3D solitons in the quasi-2D OL case are always unstable, the addition of another linear OL in the z-direction allows us to stabilize 3D solitons both for attractive and repulsive mean interactions. From our results, we suggest the possible use of spatial modulations of the nonlinearity in one of the directions as a tool for the management of stable 3D solitons.

Twisted phonons in Bose–Einstein condensates

“…This shows that nonlinear twisted phonon modes, with dark soliton envelopes, can exist in a Bose-Einstein condensate, which are different from the soliton structures usually considered in a condensate [5,6,14]. We can however find some resemblance with the case of hollow solitons considered in a cigar-shaped waveguide [15], which can occur for g < 0.…”

3D Nonlinear Localized Gap Modes in Bose‐Einstein Condensates Trapped by Optical Lattices and Space‐Periodic Nonlinear Potentials

“…From a theoretical viewpoint, 2D matter-wave gap solitons and vortical ones, both bright and dark types, have been predicted in the pancake/ disc-shaped BECs trapped by 2D optical lattice potentials. [23][24][25][26][27][28][29][30][31] 3D Weyl solitons, [32] gap solitons, and vortices of a spherical (repulsive) BEC [33,34] and a dipolar one [35] confined in 3D optical lattices have also been predicted; both 2D and 3D solitons of gap and vortical types can also be stabilized by low-dimensional optical lattices [36][37][38][39] ; self-trapping and stable multidimensional solitons supported by 2D and 3D periodic optical lattice potentials and described by the mean-field hydrodynamic model have entered the context of superfluid (degenerate) Fermi gases. [40,41] In particular, the novel 2D linear periodic lattices as parity-time (PT) symmetric potentials [42][43][44][45] and photonic Moiré lattices, [46,47] wherein both can find their optical lattices counterparts in BECs, were recently applied to stabilizing various solitons.…”

Bright solitons in Bose–Einstein condensates with field-induced dipole moments

“…Another novel and potentially important ingredient available in BEC settings is spatially periodic modulation of the local strength of the contact interactions by means of the Feshbach resonance controlled by periodically patterned laser or magnetic fields, as considered, e.g., in [18], leading to the concept of optically or magnetically induced nonlinear lattices. The nonlinearity modulation in space gives rise to new kinds of solitons and solitary vortices, as summarized in the review [19].…”