Solitons and Vortices in Atomic BECs

Andrew Martin, Nick Parker, Simon Gardiner, Charles Adams

Atomic Bose-Einstein condensates support macroscopic excitations in the form of bright solitons, dark solitons, and quantized vortices. Our research is based upon the Gross-Pitaevskii equation (GPE) which describes atomic BECs at ultracold temperature,

where ψ in the macroscopic 'wavefunction' of the condensate, V ext is the potential used to trap the atoms and the nonlinear coefficient g arises from atomic interactions. Our main research topics are summarised below:

Collisions of bright solitons

Bright solitons are localised nonlinear wavepackets which have found important applications in optical communication. Recently bright atomic solitons have been generated experimentally in atomic BECs. While an isolated soliton tends to behave as a classical particle, multiple solitons interact in a non-trivial manner. Here we study the dynamics of multiple solitons in a harmonic trap, and in particular the effect of collisions between the solitons.

Formation of vortex lattices

Recent experiments have generated vortex lattices in atomic BECs by rotating the condensate in an elliptical trap. We successfully describe the evolution using the GPE in 2D, and find 4 stages: (i) Fragmentation: an unstable quadrupole leads to the fragmentation of the condensate. (ii) Symmetry-breaking: the two-fold symmetry of the system becomes macroscopically broken. (ii) Turbulence: A disordered state of vortices and sound waves is formed, with the characteristics of Kolmogorov turbulence. (iv) Crystallisation: Through vortex-sound interactions (see below), the vortices orders themselves into a lattice.
N. G. Parker and C. S. Adams, cond-mat/0505730

Vortex-sound interactions

Accelerating vortices in atomic BECs decay via the emission of sound waves. In a harmonic trap, the inhomogeneous density causes a vortex to precess, and this induces sound emission (left, upper plots). However, in these confined systems, reabsorption of the emitted sound can occur. A dimple trap embedded in a weak outer trap can be used to control these vortex-sound interactions. By simulating these dynamics, we have shown that the power radiated is proportional to the acceleration squared. Similarly, vortices can accelerate due to the interaction with other vortices, and this also induces sound emission (left, lower plot).
N. G. Parker et al., PRL 92 , 160403 (2004)

Decay, stabilisation and parametric driving of dark solitons

Dark solitons (localised density dips) are technically 1D objects. When embedded in 3D systems they are unstable to transverse modes, and decay into vortex rings and sound waves (right, top). However, in quasi-1D geometries featuring strong transverse confinement, dark solitons are metastable to this effect.
N.P. Proukakis et al., J. Opt. B: Quantum Semiclass. Opt. 6, S380-S391 (2004)

In analogy to vortices, dark solitons radiate sound waves under acceleration, with the power emitted being proportional to the acceleration squared. In confined systems, sound reabsorption can occur, which can partially or fully stabilise this decay. By employing a dimple trap of variable depth, within a weaker trap, these soliton-sound interactions can be controlled.
N. G. Parker et al., PRL 90, 220401 (2003)

We can further manipulate the soliton-sound interactions. By 'shaking' the condensate, we can parametrically drive the dark soliton and increase its energy. This technique could be employed to stabilise the soliton against dissipation.
N. G. Parker et al. , PRL 93, 130408 (2004)