We introduce a novel mechanism to develop a turbulent flow in a spinor Bose-Einstein condensate, consisting in the stirring of a single line vortex by means of an external magnetic field. We find that density and velocity fluctuations have white-noise power spectra at large frequencies and that Kolmogorov 5/3 law is obeyed in the turbulent region. As the stirring is turned off, the flow decays to an agitated non-equilibrium state that shows an energy bottleneck crossover at small length scales. We demonstrate our findings by numerically solving two-state spinor coupled 3D Gross-Pitaevskii equations. We suggest that this mechanism may be experimentally implemented in spinor ultracold gases confined by optical traps. PACS numbers: 67.85.De, 67.85.Fg,67.25.dk 1 arXiv:1309.6218v1 [cond-mat.quant-gas] 24 Sep 2013Ever since Kolmogorov seminal ideas on classical turbulence [1], stochastic and universal laws have been sought for and discovered to be obeyed by highly complex fluid flows. Among the most celebrated predictions is the so-called "5/3" energy cascade. Although turbulence in general has remained as a fascinating topic of study both classically [2] and in helium superfluids [3,4], there has been an enormous recent interest in the study of turbulence in ultracold superfluid gases, see for recent reviews. Of notorious relevance are the experimental realizations of quantum turbulence (QT) in a superfluid ultracold 87 Rb gas in a pure magnetic trap [8], and in a 2D version confined by an annular trap [9]. In the theoretical side, a lot of effort has been devoted to understand QT as a "vortex tangle" as well as the velocity statistics of the turbulent state [10][11][12][13][14].Following the findings of Ref. [15], where it was shown that Gross-Pitaevskii (GP) spinor Bose-Einstein condensates (s-BEC) in inhomogenous optical traps can support vortices "on demand" in the presence of external magnetic fields, we study here the dynamics generated by the simple stirring of a single vortex in a 3D, spin 1/2, s-BEC. We shall show that even for mild stirrings a turbulent flow is developed in both components of s-BEC. In what follows, we describe the system and the temporal excitation protocol, as well as the nonequilibrium stationary state that it is reached once the excitation is turned-off. We discuss several scenarios.As succinctly put in Ref. [16], the study of quantum turbulence should address the following three questions: i) the generation of turbulence; ii) the statistical steady state; and, iii) the decay of turbulence. In this Letter, we analyze a novel, simple and realizable stirring procedure to produce turbulence in ultracold gases. The lack of a dissipative mechanism in GP superfluids makes it difficult to produce a true turbulent steady state, yet a turbulent phase is clearly obtained during and after the stirring process. When the latter is turned off, one finds that the flow decays to a non-equilibrium stationary state with turbulence remnants and an energy bottleneck contribution at small length scales [17]...

We present a simple mechanism to produce vortices at any desired spatial locations in harmonically trapped Bose-Einstein condensates (BEC) with multicomponent spin states coupled to external transverse and axial magnetic fields. The vortices appear at the spatial points where the spin-transverse field interaction vanishes and, depending on the multipolar magnetic field order, the vortices can acquire different predictable topological charges. We explicitly demonstrate our findings, both numerically and analytically, by analyzing a 2D BEC via the Gross-Pitaevskii equation for atomic systems with either two or three internal states. We further show that, by an spontaneous symmetry breaking mechanism, vortices can appear in any spin component, unless symmetry is externally broken at the outset by an axial field. We suggest that this scenario may be tested using an ultracold gas of $^{87}$Rb occupying all three $F = 1$ states in an optical trap.Comment: 11 pages, 9 figures, (Accepted in PRA

In 1869, Lord Kelvin found that the way vortices are knotted and linked in an ideal fluid remains unchanged in evolution, and consequently hypothesized atoms to be knotted vortices in a ubiquitous ether, different knotting types corresponding to different types of atoms. Even though Kelvin’s atomic theory turned out incorrect, it inspired several important developments, such as the mathematical theory of knots and the investigation of knotted structures that naturally arise in physics. However, in previous studies, knotted and linked structures have been found to untie via local cut-and-paste events referred to as reconnections. Here, in contrast, we construct knots and links of non-Abelian vortices that are topologically protected in the sense that they cannot be dissolved employing local reconnections and strand crossings. Importantly, the topologically protected links are supported by a variety of physical systems such as dilute Bose-Einstein condensates and liquid crystals. We also propose a classification scheme for topological vortex links, in which two structures are considered equivalent if they differ from each other by a sequence of topologically allowed reconnections and strand crossings, in addition to the typical continuous transformations. Interestingly, this scheme produces a remarkably simple classification.

Under the presence of external magnetic fields with cylindrical symmetry, Skyrmion-string defects with arbitrary topological charges are shown to appear in spinor F = 1 Bose-Einstein condensates.We show that, depending on the magnetic field boundary condition, the topological spin texture, at the planes perpendicular to the cylindrical axis, can take zero, half integer, or arbitrary values between −1/2 and 1/2. We argue that these are true topological defects since their charge is independent of the spatial location of the singularity and since the total Skyrmion charge is the sum of the individual charges of the defects present. Our findings are obtained by numerically solving the corresponding fully coupled Gross-Pitaevskii equations without any symmetry assumptions.We analyze, both, polar 23 Na and ferromagnetic 87 Rb condensates. * romero@fisica.unam.mx 1 arXiv:1703.03795v1 [cond-mat.quant-gas]

By exact numerical solutions of the Gross-Pitaevskii (GP) equation in 3D, we assess the validity of 1D and 2D approximations in the study of Bose-Einstein condensates confined in harmonic trap potentials. Typically, these approximations are performed when one or more of the harmonic frequencies are much greater than the remaining ones, using arguments based on the adiabatic evolution of the initial approximated state. Deviations from the 3D solution are evaluated as a function of both the effective interaction strength and the ratio between the trap frequencies that define the reduced dimension where the condensate is confined. The observables analyzed are both of stationary and dynamical character, namely, the chemical potential, the wave function profiles, and the time evolution of the approximated 1D and 2D stationary states, considered as initial states in the 3D GP equation. Our study, besides setting quantitative limits on approximations previously developed, should be useful in actual experimental studies where quasi-1D and quasi-2D conditions are assumed. From a qualitative perspective, 1D and 2D approximations certainly become valid when the anisotropy is large, but in addition the interaction strength needs to be above a certain threshold.