Matter-wave solitons supported by quadrupole–quadrupole interactions and anisotropic discrete lattices

Abstract

We numerically and analytically investigate the formations and features of two-dimensional discrete Bose–Einstein condensate solitons, which are constructed by quadrupole–quadrupole interactional particles trapped in the tunable anisotropic discrete optical lattices. The square optical lattices in the model can be formed by two pairs of interfering plane waves with different intensities. Two hopping rates of the particles in the orthogonal directions are different, which gives rise to a linear anisotropic system. We find that if all of the pairs of dipole and anti-dipole are perpendicular to the lattice panel and the line connecting the dipole and anti-dipole which compose the quadrupole is parallel to horizontal direction, both the linear anisotropy and the nonlocal nonlinear one can strongly influence the formations of the solitons. There exist three patterns of stable solitons, namely horizontal elongation quasi-one-dimensional discrete solitons, disk-shape isotropic pattern solitons and vertical elongation quasi-continuous solitons. We systematically demonstrate the relationships of chemical potential, size and shape of the soliton with its total norm and vertical hopping rate and analytically reveal the linear dispersion relation for quasi-one-dimensional discrete solitons.

Two-dimensional quantum droplets in binary quadrupolar condensates

“…The objective of the present work is to demonstrate that the stabilization is also possible with the help of long-range quadrupole-quadrupole interactions (QQI) between particles in BEC. Previously, the formation of solitons in QQI-coupled BEC was addressed in models that did not include the LHY terms [89][90][91][92][93], which made it more difficult to stabilize the self-trapped states in the BEC.…”

“…In [89], the creation of quadrupolar matter-wave solitons in the 2D free space was predicted, with a conclusion that, in the presence of EQQI, the solitons feature a higher mass and stronger anisotropy than their DDI-maintained counterparts, for the same environmental parameters. Possibilities of building 2D (quasi-) discrete matter-wave solitons composed of quadrupole particles trapped in deep isotropic and anisotropic optical-lattice potentials was demonstrated in [90,91], respectively. In [96], soliton solutions of the mixed-mode and semi-vortex types were constructed in binary quadrupolar BECs including spin-orbit coupling.…”

Quantum droplets in two-dimensional optical lattices

“…For example, in higher-dimensional spaces, we can construct more complex lattice structures, such as square lattices [79][80][81][82][83], triangle lattices [84][85][86] and honeycomb lattices [87][88][89][90] (graphene structure). Furthermore, in the higher-dimensional domains, we can not only consider the fundamental or the dipole modes but also the quadrupole modes [91][92][93][94][95], or more interestingly, the vortex modes. However, the dynamics of QDs in these higherdimensional spaces with periodic potential have not been considered thus far.…”

Two-Dimensional Vortex Solitons in Spin-Orbit-Coupled Dipolar Bose–Einstein Condensates

“…The other is introducing spatially periodic potentials, which is known to be able to help stabilize 2D and even 3D fundamental and vortical solitons in plentiful settings [17][18][19][20], and the spectral band these periodical potentials host can create gap solitons, as well [17,[21][22][23][24]. Another method is to use nonlocal nonlinearities, which can came from the long-range interaction between the molecules in liquid crystals [25], the diffusive behavior in nonlinear medium [26,27], the van der Waals interactions between Rydberg atoms formed in BEC [28], the dipole-dipole interaction (DDI) and quadrupolar interaction between the permanent [29,30] or the external fields' induced [31][32][33][34][35][36] magnetic or electric dipole moments of the BEC atoms.…”