Role of the mean field in Bloch oscillations of a Bose-Einstein condensate in an optical lattice and harmonic trap

Abstract

Using the Crank-Nicholson method, we study the evolution of a Bose-Einstein condensate in an optical lattice and harmonic trap. The condensate is excited by displacing it from the center of the harmonic trap. The mean field plays an important role in the Bloch-like oscillations that occur after sufficiently large initial displacement. We find that a moderate mean field significantly suppresses the dispersion of the condensate in momentum space. When the mean field becomes large, soliton and vortex structures appear in the condensate wavefunction.

Tunneling of Bose—Einstein condensate and interference effect in a harmonic trap with a Gaussian energy barrier

“…First we start the moving of the condensate by displacing it from the centre of the harmonic trapping potential in the ξ direction by a distance of ∆ξ = −15a at time τ = 0. [21] The result is shown in Fig. 1.…”

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

“…[8] For this reason, BECs confined in a combined potential, which is made of an optical lattice and a harmonic trap, were discussed. [9][10][11][12] In situations with both attractive and repulsive nonlinearities, Nikolaos et al systematically investigated the properties of lattice solitons, [9] and the evolution of a BEC soliton in an optical lattice and a harmonic trap was studied. [10] Recently, the dynamics of matter-wave solitons in harmonic traps with flashing optical lattices has also been studied analytically and numerically.…”

“…[9][10][11][12] In situations with both attractive and repulsive nonlinearities, Nikolaos et al systematically investigated the properties of lattice solitons, [9] and the evolution of a BEC soliton in an optical lattice and a harmonic trap was studied. [10] Recently, the dynamics of matter-wave solitons in harmonic traps with flashing optical lattices has also been studied analytically and numerically. [11] The motion of the solitary wave that is trapped in a potential consisting of linear magnetic and time-dependent laser fields is then manipulated by controlling the strengths of the fields.…”

“…What is more, and distinct from the 3D harmonic traps in the other combined potentials (see Refs. [9] and [10]), the 2D parabolic trap is convenient for the manipulation of the 3D vortex solitons in the unconfined direction. For the BEC vortex solitons trapped in a harmonic confinement or in a 2D axially symmetric harmonic confinement, solitary vortices and the corresponding higher-order radial states were found in both the attractive and the repulsive nonlinearities.…”

Dynamics of Bose—Einstein condensate in a harmonic potential and a Gaussian energy barrier

“…After the displacement, the condensate is away from the centre of the trap and therefore is expected to perform oscillations about the minimum of the harmonic trap. [17] We present the contour plot of the case of displacing the condensate by ∆ξ = −25 in Fig. 2.…”