Two-dimensional solitons in Bose-Einstein condensates with a disk-shaped trap

Abstract

We consider, both analytically and numerically, the evolution of two-dimensional ͑2D͒ nonlinear matterwave pulses in a Bose-Einstein condensate with a disk-shaped trap and repulsive atom-atom interactions. Due to the strong confinement in the axial direction the sound speed of the system is cϭ(1/2 1/4)c 0 , where c 0 is the corresponding value without the trap. From the 3D order-parameter equation of the condensate, we derive a soliton-bearing Kadomtsev-Petriashvili equation with positive dispersion. When the trapping potential is weak in two transverse directions, a low-depth plane dark soliton can propagate in the condensate with a changing profile but preserving its structure down to the boundary of the condensate. We show that high-depth plane dark solitons are unstable to long-wavelength transverse disturbances. The instability appears as a longitudinal modulation of the soliton amplitude decaying into vortices. We also show how a dark lumplike 2D nonlinear excitation can be excited in the system. Furthermore, a dark lump decaying algebraically in two spatial directions can propagate rather stable in the condensate, but disappears near the boundary of the condensate where two vortices are nucleated. The vortices move in opposite directions along the boundary and when meeting merge creating a new lump. Finally, we also provide results for head-on and oblique collisions of two lumps in the system.

Periodic shedding of vortex dipoles from a moving penetrable obstacle in a Bose-Einstein condensate

“…It needs to be mentioned that we cannot exclude the possibility that the crescent-shaped density dimple is a rarefaction pulse or a gray soliton, which can also propagate with preserving its density profile with a nonzero density minimum [25,[29][30][31]. When the energy accumulated by the moving obstacle is not sufficient to generate a vortex dipole, it can possibly transform into lower energy excitation.…”

Nonlinear waves in Bose–Einstein condensates: physical relevance and mathematical techniques

“…(130) relevant to the Tonks gas (corresponding to g(ρ) ∼ ρ 2 ) [159], as well as the BEC-Tonks crossover regime (corresponding to a generalized nonlinearity) [150] were derived and analyzed as well. Finally, it is relevant to note that there exist studies in higher-dimensional (diskshaped) BECs, where the RPM was used to predict 2D nonlinear structures, such as "lumps" described by an effective Kadomtsev-Petviashvili equation [274], and "dromions" described by an effective Davey-Steartson equation [275,276].…”

Dark-soliton dynamics and snake instability in superfluid Fermi gases trapped by an anisotropic harmonic potential

“…The snake stability of dark solitons of superfluid Fermi gases in the unitarity limit can be studied by monitoring the evolution of a standing dark soliton created at the trap center [52][53][54][55][56]. The development of the snake instability and the concomitant vortex rings for a wide range of the numbers of atom pairs with λ = 6.5 are displayed in Fig.4 where the superfluid density is depleted, and so the slice of the vortex ring appears as two dark spots separated vertically.…”

“…Dark solitons have 1D character, which are stable in the quasi-1D regime, but feature a long-wavelength transverse instability known as the "snake instability" [52][53][54][55][56], when extended into higher dimensions. The snake instability originates from the transfer of the soliton kinetic energy to the transverse modes parallel to the soliton nodal plane.…”

“…The snake instability originates from the transfer of the soliton kinetic energy to the transverse modes parallel to the soliton nodal plane. Generally dark solitons undergo a snake deformation, causing the nodal plane collapse into vortex rings [54][55][56] in 3D (or vortex-antivortex pairs in two dimensions [53]). For atomic BECs, it has been shown that this instability leads to a strong bending of the nodal plane, which breaks down into vortex rings and sound waves, as experimentally observed [57,58].…”