One of the actual and quickly developing spheres of modern dynamics is the turbulence theory in superfluids involving Bose-Einstein condensate (BEC) of atoms of alkaline elements. At studying the turbulence in BEC it is important to know how do vortices form and interact with each other, and what part do they play in process of transition from a condensate to a turbulence state.
One of the actual and quickly developing spheres of modern dynamics is the turbulence theory in superfluids involving Bose-Einstein condensate (BEC) of atoms of alkaline elements. At studying the turbulence in BEC it is important to know how do vortices form and interact with each other, and what part do they play in process of transition from a condensate to a turbulence state.
Turbulence in classical fluids has been the subject of scientific study for centuries, yet there is still no complete general theory of classical turbulence connecting microscopic physics to macroscopic fluid flows, and this remains one of the open problems in physics. In contrast, the phenomenon of quantum turbulence in superfluids has well-defined theoretical descriptions, based on first principles and microscopic physics, and represents a realm of physics that can connect the classical and quantum worlds. Studies of quantum turbulence may thus be viewed as a path for progress on the long-standing problem of turbulence.A dilute-gas Bose-Einstein condensate (BEC) is, in most cases, a superfluid that supports quantized vortices, the primary structural elements of quantum turbulence. BECs are particularly convenient systems for the study of vortices, as standard techniques allow the microscopic structure and dynamics of the vortices to be investigated. Vortices in BECs can be created and manipulated using a variety of techniques, hence BECs are potentially powerful systems for the microscopic study of quantum turbulence.This dissertation focuses on quantized vortices in BECs, specifically experimental and numerical studies of their formation, dynamics, and decay, in an effort to understand the microscopic nature of vortices as elements of quantum turbulence. Four main experiments were performed, and are described in the main chapters of this dissertation, after introductions to vortices, experimental methods, and turbulence are presented. These experiments were aimed at understanding various aspects of how vortices are created and behave in a superfluid system. They involved vortex dipole nucleation in the breakdown of superfluidity, persistent current generation from a turbulent state in the presence of energy dissipation, decay of angular momentum of a BEC due to trapping potential impurities, and exploration of the spontaneous formation of vortices during the BEC phase transition. These experiments represent progress towards enhanced understanding of the formation, dynamics, and decay of vortices in BECs and thus may be foundational to more general studies of quantum turbulence in superfluids.
This report addresses our recent study on pattern formation in two-component Bose-Einstein condensates(BECs), focusing on the dynamics of multiple-domain formation and the structure of vortex states in rotating condensates. Cross-phase modulation instability gives rise to formation of multiple domains that alternate two components, which are consistent with the experimental observation by the MIT group. Rotating two-component BECs exhibit a rich variety of vortex states such as square lattices and vortex sheets, which depend on the strength of intercomponent interaction and rotation frequency.
Fluid turbulence remains an open problem in contemporary physics. In gases or liquids encountered in daily life, turbulence is comprised of swirling vortices of varying sizes, shapes and strengths. The impossibility of making detailed predictions of turbulent flows comes, in part, from the complicated nature of these vortices. Turbulence in quantum mechanical superfluids, on the other hand, is comparatively simple. When stirred, a superfluid produces well-defined, discretised vortex lines, and hence turbulence in these fluids is much more straightforward to interpret. As such, there is hope that the study of vortices in superfluids may hold the key to unlocking the mysteries of turbulence.
This work rectifies the hydrodynamic equations commonly used to describe the superfluid velocity field in such a way that vortex dynamics are also taken into account. In the field of quantum turbulence, it is of fundamental importance to know the correct form of the equations which play similar roles to the Navier-Stokes equation in classical turbulence. Here, such equations are obtained by carefully taking into account the frequently overlooked multivalued nature of the U(1) phase field. Such an approach provides exact analytical explanations to some numerically observed features involving the dynamics of quantum vortices in Bose-Einstein condensates, such as the universal t1/2 behavior of reconnecting vortex lines. It also expands these results beyond the Gross-Pitaevskii theory so that some features can be generalized to other systems such as superfluid 4He, dipolar condensates, and mixtures of different superfluid systems.
After more than a decade of experiments generating and studying the physics of quantized vortices in atomic gas Bose-Einstein condensates, research is beginning to focus on the roles of vortices in quantum turbulence, as well as other measures of quantum turbulence in atomic condensates. Such research directions have the potential to uncover new insights into quantum turbulence, vortices, and superfluidity and also explore the similarities and differences between quantum and classical turbulence in entirely new settings. Here we present a critical assessment of theoretical and experimental studies in this emerging field of quantum turbulence in atomic condensates.
Abstract : The Bose-Einstein condensation (BEC) laboratory at the University of Arizona has built a program of research that focuses on two areas of BEC physics. First, we developed techniques necessary to experimentally investigate dynamic quasi-condensed states. With our system, we have instituted new directions of experimental BEC physics: studying spontaneous formation of topological defects during the BEC phase transition, and studying transitions to superfluid turbulent states. As phase transitions and turbulence occur throughout natural phenomena, this work is further relevant to a wide range of subjects in physics. Our first published results have been enabled using the support of ARO award DAAD19-03-1-0368; our research in these areas is also ongoing. Our second main efforts have revolved around refining capabilities for studying and manipulating vortices and ultra-cold gases in disc-shaped and annular potentials using optical potentials, with a particular eye towards quantum engineering of vortex and persistent current states. These efforts involve often separate areas of investigation: manipulating condensates with laser light, two-dimensional physics, fluid dynamics and turbulence, phase-transition dynamics, and vortices and persistent currents. Our efforts are collaborative, with theoretical work at multiple universities and experimental work in Arizona progressing in tandem.