Creation and mobility of discrete solitons in Bose-Einstein condensates

We analyze the generation and mobility of discrete solitons in Bose-Einstein condensates confined in an optical lattice under realistic experimental conditions. We discuss first the creation of one-dimensional discrete solitons, for both attractive and repulsive interatomic interactions. We then address the issue of their mobility, focusing our attention on the conditions for the experimental observability of the Peierls-Nabarro barrier. Finally we report on the generation of self-trapped structures in two and three dimensions. Discrete solitons may open alternative routes for the manipulation and transport of Bose-Einstein condensates.

Figure 1

Density profile of a discrete soliton (solid line) with (a) the center of mass centered in one minimum of the optical lattice and (b) the center of mass displaced by half lattice period.

Figure 2

(a) Energy of the first band in units of the recoil energy and (b) velocity profile in units of $v_r=\hslash \pi ∕md$ as a function of the quasimomentum in the first Brillouin zone for an optical potential depth of $8E_r$.

Figure 3

(a) Density profile of the ground state of a ${}^{87}\mathrm{Rb}$ condensate in the combined (magnetic and optical) trap for $N=2000$, ${\omega }_x=50\times 2\pi \text{Hz}$, ${\omega }_y={\omega }_z=92\times 2\pi \text{Hz}$, $a=5.8\text{nm}$, $V_0=1E_r$, and $d=0.8\mu \mathrm{m}$. (b) Density profile of the staggered soliton $100\text{ms}$ after the imprinting of a phase difference of $\pi$ between consecutive wells and after the magnetic trap is switched off. (c) Phase profile of the staggered soliton shown in (b).

Figure 4

Momentum associated with the PN barrier calculated with the variational method (open dots), with the imaginary time evolution of the GPE (squares), and with the DNLSE (stars). The necessary momentum to move the soliton (calculated with the real time evolution of the GPE) is displayed by the dotted line.

Figure 5

(a) Density profile of a discrete soliton created in the presence of an optical potential of depth $6E_r$ before and $21\text{ms}$ after a transfer of momentum of $0.1k_r$ is applied to the structure. (b) Density profile of the localized structure generated with a lattice of amplitude $8E_r$ (dotted line) and the corresponding density profile $10\text{ms}$ after a kick of $0.3k_r$ is given (solid line). Seventy-seven percent of the atoms remain in the reconfigured structure.

Figure 6

Spatial structure of a matter discrete localized structure created in the presence of a 3D optical lattice with a depth $V_0=6E_r$, and a period $d=1.6\mu \mathrm{m}$, as a function of two spatial coordenates, $\left(x,y\right)$, for a fixed value of the third coordinate, $z=0$.