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.
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.
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 numerically simulate the free decay of two-dimensional quantum turbulence in a large, homogeneous Bose-Einstein condensate. The large number of vortices, the uniformity of the density profile, and the absence of boundaries (where vortices can drift out of the condensate) isolate the annihilation of vortex-antivortex pairs as the only mechanism which reduces the number of vortices, Nv, during the turbulence decay. The results clearly reveal that vortex annihilation is a four-vortex process, confirming the decay law Nv ∼ t−1/3 where t is time, which was inferred from experiments with relatively few vortices in small harmonically trapped condensates.
We numerically simulate the free decay of two-dimensional quantum turbulence in a large, homogeneous Bose-Einstein condensate. The large number of vortices, the uniformity of the density profile, and the absence of boundaries (where vortices can drift out of the condensate) isolate the annihilation of vortex-antivortex pairs as the only mechanism which reduces the number of vortices, Nv, during the turbulence decay. The results clearly reveal that vortex annihilation is a four-vortex process, confirming the decay law ${N}_{\mathrm{v}}\ensuremath{\sim}{t}^{\ensuremath{-}1/3}$ where t is time, which was inferred from experiments with relatively few vortices in small harmonically trapped condensates.
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 conduct a theoretical study of the creation and dynamics of vortices in a two-dimensional binary Bose-Einstein condensate with a mass imbalance between the species. To initiate the dynamics, we use one or two rotating paddle potentials in one species, while the other species is influenced only via the interspecies interaction. In both species, the number and the dominant sign of the vortices are determined by the rotation frequency of the paddle potential. Clusters of positive and negative vortices form at a low rotation frequency comparable to that of the trap when using the single paddle potential. In contrast, vortices of the same sign tend to dominate as the rotation frequency of the paddle increases, and the angular momentum reaches a maximum value at a paddle frequency where the paddle velocity becomes equal to the sound velocity of the condensate. When the rotation frequency is sufficiently high, the rapid annihilation of vortex-antivortex pairs significantly reduces the number of vortices and antivortices in the system. For two paddle potentials rotating in the same direction, the vortex dynamics phenomenon is similar to that of a single paddle. However, when the paddle potentials are rotated in the opposite direction, both positive- and negative-signed vortices occur at all rotational frequencies. At the low rotation frequencies, the cluster of like-signed vortices produces the ${k}^{\ensuremath{-}5/3}$ and ${k}^{\ensuremath{-}3}$ power laws in the incompressible kinetic energy spectrum at low and high wave numbers, respectively, a hallmark of the quantum turbulent flows.
In a recent experiment, Kwon et al. [Phys. Rev. A 90, 063627 (2014)] generated a disordered state of quantum vortices by translating an oblate Bose-Einstein condensate past a laser-induced obstacle and studied the subsequent decay of vortex number. Using mean-field simulations of the Gross-Pitaevskii equation, we shed light on the various stages of the observed dynamics. We find that the flow of the superfluid past the obstacle leads initially to the formation of a classical-like wake, which later becomes disordered. Following removal of the obstacle, the vortex number decays due to vortices annihilating and drifting to the boundary. Our results are in excellent agreement with the experimental observations. Furthermore, we probe thermal effects through phenomenological dissipation.