Controlling quantum vortex dynamics and vortex-antivortex annihilation in Bose-Einstein condensates with optical lattices

TL;DR

This paper investigates how optical lattices influence vortex behavior in Bose-Einstein condensates, revealing new dynamics and control mechanisms for vortex-antivortex interactions in modulated superfluids.

Contribution

It provides a detailed analysis of vortex dynamics and annihilation in BECs under 1D and 2D optical lattices, highlighting the effects of lattice intensity and geometry.

Findings

Vortex energy depends on core position and energy barriers vary with lattice intensity.

Vortex dipoles exhibit distinct behaviors in 1D and 2D lattices, including annihilation and translation.

Optical lattices can reverse vortex translation velocity and induce oscillatory motions.

Abstract

Superfluids with strong spatial modulation can be experimentally produced in the area of cold atoms under the influence of optical lattices. Here we address $^{87}$Rb bosons at T=0 K in a flat geometry under the influence of a periodic potential with the Gross-Pitaevskii theory. The statics and dynamics of vortex excitations are studied in the case of one dimensional (1D) and of two dimensional (2D) optical lattices, as function of the intensity of the optical lattice. We compute how the vortex energy depends on the position of its core and the energy barrier that a vortex has to surmount in order to move in the superfluid. The dynamics of a vortex dipole, a pair of vortices of opposite chirality, differ profoundly from the case of a uniform superfluid. In the 1D case, when parallel ridges of density are present, the dynamics depends on the positions of the two vortices. If they are in the same channel between two ridges, then the two vortices approach each other until they annihilate each other in a short time. If the two vortices are in distinct channels the dipole undergoes a rigid translation but with a velocity depending on the intensity of the optical lattice and this translation velocity can even change sign with respect to the case of the uniform superfluid. Superimposed on this translation an oscillatory motion is also present. These oscillatory motions can be both longitudinal, i.e. along the channel, as well as transverse. In all cases the transverse motions are one-side, in the sense that the vortex core never crosses the equilibrium position nearest the starting position. In the case of the 2D lattices we study (square, triangular and honeycomb), the two vortices of a dipole move mainly by jumps between equilibrium positions and approach each other until annihilation.