Three-dimensional Bose—Einstein condensate vortex solitons under optical lattice and harmonic confinements

Abstract

We predict three-dimensional vortex solitons in a Bose-Einstein condensate under a complex potential, which is the combination of a two-dimensional parabolic trap along the transverse radial direction and a one-dimensional optical-lattice potential along the z axis direction. The vortex solitons are built in the form of a layer-chain structure made of several fundamental vortices along the optical-lattice direction. This has not been reported before in the three-dimensional Bose-Einstein condensate. By using a combination of the energy density functional method with direct numerical simulation, we find three-dimensional vortex solitons with topological charges χ = 1, χ = 2, and χ = 3. Moreover, the macroscopic quantum tunneling and chirp phenomena of the vortex solitons are shown in the evolution. Therein, the occurrence of macroscopic quantum tunneling provides the possibility for the experimental realization of quantum tunneling. Specifically, we successfully manipulate the vortex solitons along the optical lattice direction. The stability limits for dragging the vortex solitons from an initial fixed position to a prescribed location are further pursued.

Nonlinear tunneling through a strong rectangular barrier

“…For restricted systems, such as BECs in a harmonic trap, in a double or triple well, or in an optical lattice, some numerical or theoretical methods have been employed to solve the Gross-Pitaevskii equation (GPE), for example, two-or three-mode approximation, the symplectic method, and the particle swarm optimization (PSO) algorithm. [8][9][10][11][12][13][14] For non-restricted systems, a few methods have been proposed to deal with the nonlinear tunneling problem from various aspects, for example, involving the nonlinear effect only within the barrier, [15] or gradually increasing nonlinear interaction as BECs approaching an atomic quantum dot in a waveguide. [16] The dispersive wave shocks, formed in the upstream when BECs collide with a potential, were suggested to be studied by hydromechanics methods (Riemann invariants).…”

Phase diagram of the Fermi–Hubbard model with spin-dependent external potentials: A DMRG study

“…[9] The phase separation was studied by the mean-field theory due to the imbalanced mixture, paring symmetries, and antiferromagnetic order, [10] by the density-functional theory in a continuous system, [11] by the density-matrix renormalization group (DMRG) method [12] in a lattice system due to the component-dependent external potentials and the repulsive interactions, [13,14] and the polarizations. [15] We focus here on the optical lattice system of attractive interactions, [16][17][18] where the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) phase is one of the fascinating phenomena interested by both the experimentists [19] and theorists. [20,21,[23][24][25][26] In this paper, we study the interplay between the trapping potential imbalance and the attractive interactions in a twocomponent Fermi gas loaded in the one-dimensional (1D) optical lattices, [22,27] described by a Fermi-Hubbard model under the component-dependent external potentials.…”