Topological excitations in quantum fluids are coupled to the background sound field. This leads to a continuous exchange of energy between the two systems, as a result of which, the topological excitation can become deformed and its trajectory modified. These effects are considered in detail for dark solitons in trapped one-dimensional atomic Bose-Einstein condensates. The energy emitted by the dark soliton incident on a background potential gradient is shown to be proportional to the square of both the soliton deformation and the local soliton acceleration. Depending on the trap geometry, this energy can be partly or fully reabsorbed by the soliton, thus affecting its stability. The extension to vortices in trapped atomic condensates is discussed.
Topological excitations in quantum fluids are coupled to the background sound field. This leads to a continuous exchange of energy between the two systems, as a result of which, the topological excitation can become deformed and its trajectory modified. These effects are considered in detail for dark solitons in trapped one-dimensional atomic Bose-Einstein condensates. The energy emitted by the dark soliton incident on a background potential gradient is shown to be proportional to the square of both the soliton deformation and the local soliton acceleration. Depending on the trap geometry, this energy can be partly or fully reabsorbed by the soliton, thus affecting its stability. The extension to vortices in trapped atomic condensates is discussed.
Topological excitations in quantum fluids are coupled to the background sound field. This leads to a continuous exchange of energy between the two systems, as a result of which, the topological excitation can become deformed and its trajectory modified. These effects are considered in detail for dark solitons in trapped one-dimensional atomic Bose-Einstein condensates. The energy emitted by the dark soliton incident on a back-ground potential gradient is shown to be proportional to the square of both the soliton deformation and the local soliton acceleration. Depending on the trap geometry, this energy can be partly or fully reabsorbed by the soliton, thus affecting its stability. The extension to vortices in trapped atomic condensates is discussed.
Dilute atomic Bose-Einstein condensates support intriguing macroscopic excitations in the form of quantized vortices and dark solitons. In this thesis we present extensive quantitative studies of the dynamics of these phenomena in the limit of zero temperature, performed by numerical simulation of the Gross- Pitaevskii equation. We show that vortices and dark solitons are inherently unstable to acceleration through the condensate, leading to the emission of sound waves. Indeed, for a single vortex/soliton, the power emitted is proportional to the square of the local acceleration. However, due to the finite size of the condensate, the vortex/soliton reinteracts with the emitted sound. This coupling has an important effect on the ensuing dynamics, and we illustrate how it can be engineered to induce net decay, stabilise, or even drive energy into the vortex/soliton. Under the harmonic confinement typically employed to trap the condensates, the acceleration-induced decay is stabilised by reabsorption of the emitted sound. However, by modifying the trap geometry, e.g. by adding an inner dimple in which the soliton resides or an optical lattice potential, it is possible to break this equilibrium and so induce a net decay of the vortex/soliton in a controllable manner. The decay rate can be considerable and should be observable under current experimental conditions. The dynamical stability of quantized vortices is also relevant to the field of turbulence in superfluid Helium, where the motion of the vortices is induced by the surrounding distribution of vortices rather than density. We extend these results to this field, and additionally consider the interactions between two and three vortices, which are also found to involve sound emission. By exciting the sound field of the condensate it is possible to drive parametrically energy into a dark soliton. In a real dissipative environment, this can be used to stabilise the soliton decay. Finally, we illustrate the links between dark solitons and vortices: a dark soliton embedded in a three-dimensional system is prone to decay into vortex rings, while a vortex in a quasi-one-dimensional geometry cannot be supported and exists as a hybrid between a vortex and dark soliton, known as a solitonic vortex.
Dilute atomic Bose-Einstein condensates are inherently nonlinear systems and support solitary wave solutions. An important distinction from optical systems is the inhomogeneous background density, which results from the traps used to confine the atoms. As in optical systems, dark solitary waves in three-dimensional geometries are unstable to transverse excitations, which lead to a bending of the dark soliton plane and decay into vortex rings. Highly elon-gated geometries can now be achieved experimentally, in which the condensate dynamics are effectively one-dimensional, and the motion of the dark soliton is governed by the inhomogeneous longitudinal density. We show that a dark soliton is fundamentally unstable to such a changing background density, by means of numerical simulations of the soliton under various potentials (e.g. steps, ramps, harmonic traps, and optical lattices). This leads to the emission of radiation in the form of sound waves. The power emitted is found to be proportional to the square of the soliton acceleration. The latter quantity is shown to be proportional to the deformation of the apparent soliton profile, arising from the sound field in the region of the soliton. We demonstrate that the ensuing interactions between the soliton and sound field, and therefore the dynamics of the soliton, can be controlled experimentally via manipulation of the emitted sound, achieved by modifying the trap geometry. In this manner, it is possible to induce a rapid decay of the soliton, stabilise the soliton, or even pump energy into the soliton by means of parametric driving. 1
A dark soliton becomes unstable when it is incident on a background density gradient, and the induced instability results in the emission of sound. Detailed quantitative studies of sound emission are performed for various potentials, such as steps, linear ramps and Gaussian traps. The amount of sound emission is found to be a significant fraction of the soliton energy for typical potentials. Continuous emission of sound is found to lead to an apparent deformation of the soliton profile. The power emitted by the soliton is shown to be parametrized by the square of the displacement of the centre of mass of the soliton from its density minimum, thus highlighting the significance of the inhomogeneity-induced soliton deformation.
A dark soliton becomes unstable when it is incident on a background density gradient, and the induced instability results in the emission of sound. Detailed quantitative studies of sound emission are performed for various potentials, such as steps, linear ramps and Gaussian traps. The amount of sound emission is found to be a significant fraction of the soliton energy for typical potentials. Continuous emission of sound is found to lead to an apparent deformation of the soliton profile. The power emitted by the soliton is shown to be parametrized by the square of the displacement of the centre of mass of the soliton from its density minimum, thus highlighting the significance of the inhomogeneity-induced soliton deformation.
The motion of a dark soliton is investigated in a one-dimensional dilute Bose–Einstein condensate confined in a harmonic trap and an optical lattice. The harmonic trap induces a dynamical instability of the soliton, culminating in sound emission. The presence of the perturbing optical lattice enhances the instability, and in addition, dephases the emitted sound waves, thus preventing stabilization of the soliton by sound reabsorption. This instability can be probed experimentally by monitoring the soliton oscillations under various lattice configurations, which can be realized by changing the intensity and angle between the laser beams that form the lattice. For short enough times, such that the emitted sound does not reinteract with the soliton, the power emitted by the soliton is found to be proportional to the square of the local soliton acceleration, which is in turn proportional to the deformation of the soliton profile.