The generation of dark solitons in Bose-Einstein condensates has been an area of interest since the first experimental condensates were produced. The ubiquity of solitons in the natural world makes them an important phenomenon to understand. Despite excellent theoretical work in two dimensional dark solitons, few experiments have had the opportunity to investigate this regime. The work presented investigates the generation of dark solitons in a Rb-87 Bose-Einstein condensate. The evolution and decay of these topological excitations are investigated. The decay of the dark solitons is found to vary with the phase-step used to generate them. Dark solitons created with a phase-step width of 0.60 ±0.15 μm are found to decay into vortices after 10 ms. Dark solitons generated with larger phase-steps are found not to exhibit this vortex decay, instead dissipating over 10-15 ms back into the condensate. The first experimental generation of two dimensional Jones-Roberts solitons is reported in this work. These dark solitons differ from the standard planar dark soliton in that they are finite in extent and are \nfound to be more dynamically stable. The Jones-Roberts solitons are observed for 40 ms with no observed change in energy. \n
The generation of dark solitons in Bose-Einstein condensates has been an area of interest since the first experimental condensates were produced. The ubiquity of solitons in the natural world makes them an important phenomenon to understand. Despite excellent theoretical work in two dimensional dark solitons, few experiments have had the opportunity to investigate this regime. The work presented investigates the generation of dark solitons in a Rb-87 Bose-Einstein condensate. The evolution and decay of these topological excitations are investigated. The decay of the dark solitons is found to vary with the phase-step used to generate them. Dark solitons created with a phase-step width of 0.60 ±0.15 μm are found to decay into vortices after 10 ms. Dark solitons generated with larger phase-steps are found not to exhibit this vortex decay, instead dissipating over 10-15 ms back into the condensate. The first experimental generation of two dimensional Jones-Roberts solitons is reported in this work. These dark solitons differ from the standard planar dark soliton in that they are finite in extent and are \nfound to be more dynamically stable. The Jones-Roberts solitons are observed for 40 ms with no observed change in energy. \n
Summary form only given. Bose-Einstein condensates (BEC) of weakly interacting gases allow for the new regime of nonlinear atom optics. Of special interest are macroscopically excited states like dark solitons or vortices. Solitons, as particle like excitations of matter wave fields, provide a link from condensate physics to fluid mechanics, nonlinear optics and fundamental particle physics. Dark solitons in matter waves are characterized by a local density minimum and, a steep phase gradient of the wavefunction at the position of the minimum. We report on experimental and theoretical investigation of dark solitons in BECs of /sup 87/Rb which are produced by the method of phase imprinting. A highly anisotropic confining potential allows us to be close to the (quasi) 1D situation where dark solitons are expected to be dynamically stable. By monitoring the evolution of the density profile we observe the evolution of density minima travelling at a smaller velocity than the speed of sound. By comparison to analytical and numerical solutions of the 3D Gross-Pitaevskii equation for our experimental conditions we identify these density minima to be moving dark solitons. We have studied in detail the creation and the dynamics of dark solitons as a function of evolution time and imprinted phase.
Jones-Roberts solitons are the only known class of stable dark solitonic solutions of the nonlinear Schrödinger equation in two and three dimensions. They feature a distinctive elongated elliptical shape that allows them to travel without change of form. By imprinting a triangular phase pattern, we experimentally generate two-dimensional Jones-Roberts solitons in a three-dimensional atomic Bose-Einstein condensate. We monitor their dynamics, observing that this kind of soliton is indeed not affected by dynamic (snaking) or thermodynamic instabilities, that instead make other classes of dark solitons unstable in dimensions higher than one. Our results confirm the prediction that Jones-Roberts solitons are stable solutions of the nonlinear Schrödinger equation and promote them for applications beyond matter wave physics, like energy and information transport in noisy and inhomogeneous environments.
Soliton is an exotic topological excitation, and it widely exists in various nonlinear systems, such as nonlinear optics, Bose-Einstein condensates, classical and quantum fluids, plasma, magnetic materials, etc. A stable soliton can propagate with constant amplitude and velocity, and maintain its shape. Two-dimensional and three-dimensional solitons are usually hard to stabilize, and how to realize stable two-dimensional or three-dimensional solitons has aroused the great interest of the researchers. Ring dark soliton is a kind of two-dimensional soliton, which was first theoretically predicted and experimentally realized in nonlinear optical systems. Compared with the usual two-dimensional solitons, ring dark solitons have good stability and rich dynamical behaviors. Owing to their highly controllable capability, Bose-Einstein condensates provide a new platform for studying the ring dark solitons. Based on the recent progress in Bose-Einstein condensates and solitons, this paper reviews the research on the analytic solutions, stability, as well as the decay dynamics of ring dark solitons in Bose-Einstein condensates. A transform method is introduced, which generalizes the analytic solutions of ring dark solitons from a homogeneous system with time-independent nonlinearity to a harmonically trapped inhomogeneous system with time-dependent nonlinearity. The stability phase diagram of the ring dark soliton under deformation perturbations is discussed by numerically solving the Gross-Pitaevskii equations in the mean-field theory. A method of enhancing the stability of ring dark solitons by periodically modulating the nonlinear coefficients is introduced. It is also shown that the periodically modulated nonlinear coefficient can be experimentally realized by the Feshbach resonance technology. In addition, we discuss the dynamics of the decay of ring dark solitons. It is found that the ring dark soliton can decay into various vortex clusters composed of vortices and antivortices. This opens a new avenue to the investigation of vortex dynamics and quantum turbulence. It is also found that the ring dark solitons combined with periodic modulated nonlinearity can give rise to the pattern formation, which is an interesting nonlinear phenomenon widely explored in all the fields of nature. Finally, some possible research subjects about ring dark solitons in future research are also discussed.
We have created spatial dark solitons in two-component Bose-Einstein condensates in which the soliton exists in one of the condensate components and the soliton nodal plane is filled with the second component. The filled solitons are stable for hundreds of milliseconds. The filling can be selectively removed, making the soliton more susceptible to dynamical instabilities. For a condensate in a spherically symmetric potential, these instabilities cause the dark soliton to decay into stable vortex rings. We have imaged the resulting vortex rings.
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.
In this Thesis, we study various aspects of ring dark solitons (RDSs) in quasi-two-dimensional toroidally trapped Bose-Einstein condensates, focussing on atomic realisations thereof. Unlike the well-known planar dark solitons, exact analytic expressions for RDSs are not known. We address this problem by presenting exact localized soliton-like solutions to the radial Gross-Pitaevskii equation. To date, RDSs have not been experimentally observed in cold atomic gases, either. To this end, we propose two protocols for their creation in experiments. It is also currently well known that in dimensions higher than one, (ring) dark solitons are susceptible, in general, to an irreversible decay into vortex-antivortex pairs through the snake instability. We show that the snake instability is caused by an unbalanced quantum pressure across the soliton's notch, linking the instability to the Bogoliubov-de Gennes spectrum. In particular, if the angular symmetry is maintained (or the toroidal trapping is restrictive enough), we show that the RDS is stable (long-lived with a lifetime of order seconds) in two dimensions. Furthermore, when the decay does take place, we show that the snake instability can in fact be reversible, and predict a previously unknown revival phenomenon for the original (many-)RDS system: the soliton structure is recovered and all the point-phase singularities (i.e. vortices) disappear. Eventually, however, the decay leads to an example of quantum turbulence; a quantum example of the laminar-to-turbulent type of transition.