In this thesis, we numerically investigate quantum turbulence in trapped atomic Bose-Einstein condensates (BECs). We first discuss the appropriate qualitative characterization of turbulence in these systems, showing the limitation of analogies with classical hydrodynamics and turbulence in large superfluid Helium experiments. Due to their lack of available length scales, our investigated systems can only fit the ultraquantum (or Vinen) type of quantum turbulence. Secondly, we propose experimentally feasible schemes for more controlled investigations of turbulence making use of dynamical instability of multicharged vortices as an onset for complex vortex dynamics. In two dimensions, our suggested scheme allows control over vortex polarization in the harmonically trapped system. This setup is then used to study how turbulence decays in such a scenario, through the phenomenological modeling of a vortex-number rate equation. As a consequence, we were able to identify that vortex annihilation in these trapped systems happens through a four-vortex process. For three dimensions, we have first provided a study on the decay of a quadruply-charged vortex, also in a harmonically trapped BEC. Having this setting as a comparison point, we propose a quasi-isotropic turbulent system, starting from a phase-imprinted initial state of two doubly-charged, anti-parallel vortices. The vortex turbulence arisen from such configuration was shown to agree with the Vinen turbulent regime, after we characterized specific features of its decay, such as the energy spectrum [E(k) ∼ k1] and the time evolution of the vortex-line density [L(t) ∼ t1]. Although these features have been frequently verified in the context of superfluid Helium turbulence, here this identification was for the first time done for realistic, trapped atomic BECs.
In this thesis, we numerically investigate quantum turbulence in trapped atomic Bose-Einstein condensates (BECs). We first discuss the appropriate qualitative characterization of turbulence in these systems, showing the limitation of analogies with classical hydrodynamics and turbulence in large superfluid Helium experiments. Due to their lack of available length scales, our investigated systems can only fit the ultraquantum (or Vinen) type of quantum turbulence. Secondly, we propose experimentally feasible schemes for more controlled investigations of turbulence making use of dynamical instability of multicharged vortices as an onset for complex vortex dynamics. In two dimensions, our suggested scheme allows control over vortex polarization in the harmonically trapped system. This setup is then used to study how turbulence decays in such a scenario, through the phenomenological modeling of a vortex-number rate equation. As a consequence, we were able to identify that vortex annihilation in these trapped systems happens through a four-vortex process. For three dimensions, we have first provided a study on the decay of a quadruply-charged vortex, also in a harmonically trapped BEC. Having this setting as a comparison point, we propose a quasi-isotropic turbulent system, starting from a phase-imprinted initial state of two doubly-charged, anti-parallel vortices. The vortex turbulence arisen from such configuration was shown to agree with the Vinen turbulent regime, after we characterized specific features of its decay, such as the energy spectrum [E(k) ∼ k1] and the time evolution of the vortex-line density [L(t) ∼ t1]. Although these features have been frequently verified in the context of superfluid Helium turbulence, here this identification was for the first time done for realistic, trapped atomic BECs.
In this thesis, we numerically investigate quantum turbulence in trapped atomic Bose-Einstein condensates (BECs). We first discuss the appropriate qualitative characterization of turbulence in these systems, showing the limitation of analogies with classical hydrodynamics and turbulence in large superfluid Helium experiments. Due to their lack of available length scales, our investigated systems can only fit the ultraquantum (or Vinen) type of quantum turbulence. Secondly, we propose experimentally feasible schemes for more controlled investigations of turbulence making use of dynamical instability of multicharged vortices as an onset for complex vortex dynamics. In two dimensions, our suggested scheme allows control over vortex polarization in the harmonically trapped system. This setup is then used to study how turbulence decays in such a scenario, through the phenomenological modeling of a vortex-number rate equation. As a consequence, we were able to identify that vortex annihilation in these trapped systems happens through a four-vortex process. For three dimensions, we have first provided a study on the decay of a quadruply-charged vortex, also in a harmonically trapped BEC. Having this setting as a comparison point, we propose a quasi-isotropic turbulent system, starting from a phase-imprinted initial state of two doubly-charged, anti-parallel vortices. The vortex turbulence arisen from such configuration was shown to agree with the Vinen turbulent regime, after we characterized specific features of its decay, such as the energy spectrum [E(k) ∼ k1] and the time evolution of the vortex-line density [L(t) ∼ t1]. Although these features have been frequently verified in the context of superfluid Helium turbulence, here this identification was for the first time done for realistic, trapped atomic BECs.
We investigate a procedure to generate turbulence in a trapped Bose-Einstein condensate which takes advantage of the decay of multicharged vortices to reduce surface oscillations. We show that the resulting singly charged vortices twist around each other, intertwined in the shape of helical Kelvin waves, which collide and undergo vortex reconnections, creating a disordered vortex state. By examining the velocity statistics, the energy spectrum, the correlation functions, and the temporal decay and comparing these properties with the properties of classical turbulence and observations in superfluid helium, we conclude that this disordered vortex state can be identified with the Vinen regime of turbulence which has been discovered in the context of superfluid helium.
Abstract Chapter 5 delves into quantum turbulence in superfluid helium and atomic Bose-Einstein condensates (BECs). The foundation of quantum turbulence research lies in classical fluid dynamics and turbulence, which is why we begin by covering essential concepts like the Reynolds number and Kolmogorov’s -5/3 power law in the energy spectrum. These principles are crucial for understanding quantum turbulence. We then explore the shared aspects of quantum turbulence in superfluid helium and atomic BECs, such as the differences in vortex configurations compared to classical turbulence, energy spectra, cascades, and the distinction between quasiclassical (Kolmogorov) and ultraquantum (Vinen) turbulence, focusing on their decay behaviors. In superfluid helium, we emphasize experimental studies in thermal counterflow and numerical simulations using the Vortex Filament Model (VFM). The advent of visualization experiments in the mid-2000s was transformative, allowing the observation of normal fluid velocity profiles and accelerations via tracer particles, which led to more accurate simulations coupling the VFM with normal fluid dynamics. Another significant topic is the energy spectrum of quantum turbulence, and whether it mirrors classical turbulence remains a key question. In addition to thermal counterflow, localized quantum turbulence generated by oscillating objects has been a major area of study. We present research showing how quantized vortices grow and evolve into turbulence. Superfluid 3He-B also provides a platform for quantum turbulence, with advancements in microfabrication bringing MEMS and NEMS into focus for studying quantum hydrodynamics at micro- and nanoscale, influenced by boundary conditions. In atomic BECs, confined by potentials, turbulence is induced through techniques like shaking or moving potentials. A unique aspect of BECs is two-dimensional quantum turbulence, featuring inverse energy cascades, Onsager vortices, and negative temperature states. Finally, atomic BECs, being compressible, serve as a platform for both vortex and wave turbulence. Multicomponent BECs, such as spinor BECs, introduce spin turbulence, further diversifying the field.
We numerically model turbulence in a trapped atomic Bose-Einstein condensate by solving the Gross-Pitaevskii nonlinear Schroedinger equation. We find that, after an initial growth, the vortex length decays approximately as t(-1) where t is time, consistent with experiments in turbulent superfluid helium, and that the velocity components obey power-law statistics, again in agreement with observations in turbulent superfluid helium. We find the same statistics, which contrasts to the Gaussian statistics observed in ordinary classical turbulence, in a variety of quantum fluids in two and three dimensions (trapped condensates, homogeneous condensates, vortex points, vortex filaments). We argue that the non-Gaussianity arises from the singular nature of quantised vorticity.
The extension of quantum phenomena into macroscopic scales is responsible for a whole class of effects such as superconductivity, superfluidity, and Bose-Einstein condensation, which played central roles in physics throughout the last century.The production of the first Bose-Einstein condensates made possible the realization of experiments involving macroscopic quantum phenomena with an unprecedented level of control of the external parameters.The persistent currents in condensates are intimately related to the nucleation of quantized vortices, which are topological defects as response to transference of quanta of angular momentum.A conventional method for generation of such defects consists in confining the condensed atomic cloud into a rotating trap.It turns out that, for angular velocities higher than a critical value, vortex states become energetically favorable, thus inducing the creation of quantized vortices.Experimental realizations of condensed alkali-metal atoms confined by more general time-dependent potentials allowed the observation not only of vortex lattices but also of quantum turbulence.Since quantum turbulence is characterized by the presence of a self-interacting tangle of quantized vortices, the correct understanding of dynamics, formation, and stability of vortices has shown to be of paramount importance being the subject of many theoretical works.In particular, the role of acoustic excitations generated by decaying multi-charged vortices in the development of turbulence is still an open question.This work aims to provide a set of tools that helps to identify the presence as well as the charge of vortices in non-turbulent clouds observed using time-of-flight pictures.We have done a detailed study of condensates containing multi-charged vortices placed at its center where time-of-flight dynamics is only one point of our interest.Due to the control that this system provides experimentally, the collective modes become an important description since they can be excited using well stablished experimental methods as such as modulation of the s-wave scattering length, and they can also be responsible to vortex decaying.For such purposes we have used the semi-analytical variational method, and the fully numerical calculation of Gross-Pitaevskii equation.Thus we have describes the collective modes that couples dynamics of vortex with the oscillation of external components of condensed atomic cloud as well as the effects in time-of-flight.The angular momentum acts increasing the kinetic energy around the vortex core, which results in a faster expansion of perpendicular direction to it.This situation shifts the frequencies of collective oscillations of a vortex-free state, and generates richer collective modes due the coupling.Now there are four possible modes, being two types of monopole mode and two types of quadrupole modes.The difference among these types is the phase of vortex oscillation.When one considers fluctuations without polar symmetry, their collective modes result in the vortex decaying.In order to control and prevent these processes we have proposed three dynamical mechanisms such as modulation of s-wave scattering length, modulation of frequencies of harmonic trap, and modulation of the amplitude of Laguerre-Gauss potential.The last one has proven to be more effective.
We propose a scheme for generating two-dimensional turbulence in harmonically trapped atomic condensates with the novelty of controlling the polarization (net rotation) of the turbulence. Our scheme is based on an initial giant (multicharged) vortex which induces a large-scale circular flow. Two thin obstacles, created by blue-detuned laser beams, speed up the decay of the giant vortex into many singly quantized vortices of the same circulation; at the same time, vortex-antivortex pairs are created by the decaying circular flow past the obstacles. Rotation of the obstacles against the circular flow controls the relative proportion of positive and negative vortices, from the limit of strongly anisotropic turbulence (almost all vortices having the same sign) to that of isotropic turbulence (equal number of vortices and antivortices). Using this scheme, we numerically study the decay of two-dimensional quantum turbulence as a function of the polarization. Finally, we present a model for the decay rate of the vortex number which fits our numerical experiment curves, with the novelty of taking into account polarization time dependence.