We show that the interaction between vortices and sound waves in atomic Bose-Einstein condensates can be elucidated in a double-well trap: With one vortex in each well, the sound emitted by each precessing vortex can be driven into the opposing vortex (if of the same polarity). This cross talk leads to a periodic exchange of energy between the vortices which is long range and highly efficient. The increase in vortex energy (obtained by simulations of the Gross-Pitaevskii equation) is experimentally observable as a migration of the vortex to higher density over just a few precession periods. Similar effects can be controllably engineered by introducing a precessing localized obstacle into one well as an artificial generator of sound, thereby demonstrating the parametric driving of energy into a vortex.
We show that the interaction between vortices and sound waves in atomic Bose-Einstein condensates can be elucidated in a double-well trap: With one vortex in each well, the sound emitted by each precessing vortex can be driven into the opposing vortex (if of the same polarity). This cross talk leads to a periodic exchange of energy between the vortices which is long range and highly efficient. The increase in vortex energy (obtained by simulations of the Gross-Pitaevskii equation) is experimentally observable as a migration of the vortex to higher density over just a few precession periods. Similar effects can be controllably engineered by introducing a precessing localized obstacle into one well as an artificial generator of sound, thereby demonstrating the parametric driving of energy into a vortex.
The dynamics of vortex in a trapped quasi-two-dimensional Bose-Einstein condensate (BEC), which produce vortex-sound interaction was discussed. It was observed that a vortex precession in a trapped quasi-2D BEC at low temperature emits dipolar radiation, which becomes modified into a spiral wave pattern due to the motion of the vortex. The results show that the vortex energy decays at a rate proportional to its acceleration squared and inversely proportional to the precession frequency. It was suggested that sound emission and reabsorption can be controlled by varying the depth of the dimple.
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.
The low temperature dynamics of a vortex in a trapped quasi-two-dimensional Bose-Einstein condensate are studied quantitatively. Precession of an off-centered vortex in a dimple trap, embedded in a weaker harmonic trap, leads to the emission of sound in a dipolar radiation pattern. Sound emission and reabsorption can be controlled by varying the depth of the dimple. In a shallow dimple, the power emitted is proportional to the vortex acceleration-squared over the precession frequency, whereas for a deep dimple, periodic sound reabsorption stabilizes the vortex against radiation-induced decay.
We have performed numerical simulations of various vortex configurations in a trapped BoseEinstein condensate by solving the two-dimensional Gross-Pitaevskii equation in the presence of a simple model of interaction between the condensate and the finite temperature thermal cloud that surrounds it. In that interaction the non-condensed thermal cloud acts as a source of dissipation with a damping effect of excitations. In the case ora single vortex and a vortex - anti vortex pair, we have found that the path of the vortices depends on the initial position, the initial separation distance if the case of two vortices and dissipation. This motion is periodic and it was found that sound waves are created by vortex motion; the intensity was stronger when the initial vortex separation distance was smaller. We have calculated the sound energy as the difference between the kinetic energy and the vortex energy. With no dissipation the vortices followed the same path with a slight oscillation due to the sound waves. We found that the smaller the initial vortex separation distance do is, the larger the sound production. The period, frequency, translation speed, sound energy and vortex energy were measured for different initial separation distances do and for different dissipation parameters 'Y. In the case of motion of one vortex, the connection between the dissipation 'Y and the friction coefficients, a and a' was studied as well. To create a simple turbulent state, we put eight pairs of vortex - anti vortex at random positions in the condensate with initial separation distance do =1.8 between them. 'Ve have studied the decay rate of the total energy, kinetic energy, quantum energy, trap energy and the z - component of the angular momentum together with the increase rate of the internal energy. Finally, we finished our investigation by putting randomly vortex - anti vortex pairs and studied the decrease of the number of vortices with time t. We found that the decrease is exponential.
We investigate the quantum tunneling of a Bose-Einstein condensate confined in a optical trap. We show that periodic pulses of coherent matter are emitted from the trap by using an oscillating energy barrier. Moreover, the emitted fraction of condensed atoms strongly increases if the period of oscillation of the height of the energy barrier is in parametric resonance with the period of oscillation of the center of mass of the condensate inside the potential well. Our model is analyzed by numerically solving the nonpolynomial Schrodinger equation (NPSE), an effective one-dimensional equation which describes the macroscopic wavefunction of Bose condensates under transverse harmonic confinement. The range of validity of NPSE is discussed and compared with that of Gross-Pitaevskii equation.
A dark soliton oscillating in an elongated harmonically confined atomic Bose-Einstein condensate continuously exchanges energy with the sound field. Periodic optical paddles are employed to controllably enhance the sound density and transfer energy to the soliton, analogous to parametric driving. In the absence of damping, the amplitude of the soliton oscillations can be dramatically reduced, whereas with damping, a driven soliton equilibrates as a stable soliton with lower energy, thereby extending the soliton lifetime up to the lifetime of the condensate.