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arXiv:2205.14654 · Physical Review A

Vortex generation in stirred binary Bose-Einstein condensates

Anacé N. da Silva, R. Kishor Kumar, Ashton S. Bradley, Lauro Tomio

Published Mar 15, 2023• 12 citations
arXivHTMLPDF

Abstract

Binary Bose-Einstein condensates of two distinct atomic species are studied, with interesting effects being verified due to the imbalance of atomic masses. We study the formation of vortices and associated turbulence flows created by stirring two mass-imbalanced coupled Bose-Einstein condensates in the miscible regime. We consider the mixture in the laboratory frame, confined in a pancake-like harmonic trap slightly perturbed elliptically by a time-dependent periodic potential, which introduces turbulent dynamics with final stable patterns of vortices, induced by the periodicity of the perturbation. Derived rotational frequencies are shown to be associated with the observed vortex patterns in the asymptotic regime, with a correspondence between the stirring procedure and a direct time-independent approach being indicated. It was also confirmed that a larger pattern of vortices is supported by the higher mass condensed species at the same frequency. For the experimentally accessible mixtures $^{85}\mathrm{Rb}\text{\ensuremath{-}}^{133}\mathrm{Cs}$ and $^{85}\mathrm{Rb}\text{\ensuremath{-}}^{87}\mathrm{Rb}$, we numerically solve the equations of motion and analyze the system dynamics using a range of measures including energy spectra. In the transient turbulent regime, spectral analysis shows evidence for the characteristic ${k}^{\ensuremath{-}5/3}$ Kolmogorov classical law associated with turbulence, modified by the universal ${k}^{\ensuremath{-}3}$ vortex core scaling in the ultraviolet regime.

DOI
10.1103/physreva.107.033314

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•Sep 19, 2017•0 citations
Binary Bose-Einstein condensates of two distinct atomic species are studied, with interesting effects being verified due to the imbalance of atomic masses. We study the formation of vortices and associated turbulence flows created by stirring two mass-imbalanced coupled Bose-Einstein condensates in the miscible regime. We consider the mixture in the laboratory frame, confined in a pancake-like harmonic trap slightly perturbed elliptically by a time-dependent periodic potential, which introduces turbulent dynamics with final stable patterns of vortices, induced by the periodicity of the perturbation. Derived rotational frequencies are shown to be associated with the observed vortex patterns in the asymptotic regime, with a correspondence between the stirring procedure and a direct time-independent approach being indicated. It was also confirmed that a larger pattern of vortices is supported by the higher mass condensed species at the same frequency. For the experimentally accessible mixtures 85Rb\ensuremath-133Cs^{85}\mathrm{Rb}\text{\ensuremath{-}}^{133}\mathrm{Cs}85Rb\ensuremath-133Cs and 85Rb\ensuremath-87Rb^{85}\mathrm{Rb}\text{\ensuremath{-}}^{87}\mathrm{Rb}85Rb\ensuremath-87Rb, we numerically solve the equations of motion and analyze the system dynamics using a range of measures including energy spectra. In the transient turbulent regime, spectral analysis shows evidence for the characteristic k\ensuremath−5/3{k}^{\ensuremath{-}5/3}k\ensuremath−5/3 Kolmogorov classical law associated with turbulence, modified by the universal k\ensuremath−3{k}^{\ensuremath{-}3}k\ensuremath−3 vortex core scaling in the ultraviolet regime.
We study two-dimensional quantum turbulence in miscible binary Bose-Einstein condensates in either a harmonic trap or a steep-wall trap through the numerical simulations of the Gross-Pitaevskii equations. The turbulence is generated through a Gaussian stirring potential. When the condensates have unequal intracomponent coupling strengths or asymmetric trap frequencies, the turbulent condensates undergo a dramatic decay dynamics to an interlaced array of vortex-antidark structures, a quasiequilibrium state, of like-signed vortices with an extended size of the vortex core. The time of formation of this state is shortened when the parameter asymmetry of the intracomponent couplings or the trap frequencies is enhanced. The corresponding spectrum of the incompressible kinetic energy exhibits two noteworthy features: (i) a ${k}^{\ensuremath{-}3}$ power law around the range of the wave number determined by the spin healing length (the size of the extended vortex core) and (ii) a flat region around the range of the wave number determined by the density healing length. The latter is associated with the small scale phase fluctuation relegated outside the Thomas-Fermi radius and is more prominent as the strength of intercomponent interaction approaches the strength of intracomponent interaction. We also study the impact of the intercomponent interaction to the cluster formation of like-signed vortices in an elliptical steep-wall trap, finding that the intercomponent coupling gives rise to the decay of the clustered configuration.
Counter-rotating vortices in miscible two-component Bose-Einstein condensates, in which superflows counter-rotate between the two components around the overlapped vortex cores, are studied theoretically in a pancake-shaped potential. In a linear stability analysis with the Bogoliubov--de Gennes model, we show that counter-rotating vortices are dynamically unstable against splitting into multiple vortices. The instability shows characteristic behaviors as a result of counter-superflow instability, which causes relaxation of relative flows between the two components in binary condensates. The characteristic behaviors are completely different from those of multiquantum vortices in single-component Bose-Einstein condensates; the number of vortices generated by the instability can become larger than the initial winding number of the counter-rotating vortex. We also investigate the nonlinear dynamics of the instability by numerically solving the Gross-Pitaevskii equations. The nonlinear dynamics drastically changes when the winding number of counter-rotating vortices becomes larger, which lead to nucleation of vortex pairs outside of the vortex core. The instability eventually develops into turbulence after the relaxation of the relative rotation between the two components.
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.
We study the stability of vortices in a binary system of Bose-Einstein condensat es, with their wave functions modeled by a set of coupled, time-dependent Gross-Pitaevskii equations. Beginning with an effective two-dimensional system, we identify miscible and immiscible regimes characterized by the inter- and intra-atomic interactions and the initial configuration of the system. We then consider a binary system of Bose-Einstein condensates placed in a rotating harmonic trap and study the single united vortex state in this system. We derive an approximate form for the energy of a single united vortex in the binary system and the critical angular velocity for the global stability of a vortex at the center of the trap. We also compute the metastability onset angular velocity for the local stability of a vortex at the center of the trap. Numerical solutions to the Gross-Pitaevskii equations support these expressions. These rotational results inform us of a novel bimodal formation within the miscible regime of the binary condensate system. We thus demonstrate the nontrivial aspects of vortex stability in interacting binary Bose-Einstein condensates as a result of their nonlinear interactions.
We investigate two-dimensional turbulence in finite-temperature trapped Bose-Einstein condensates within damped Gross-Pitaevskii theory. Turbulence is produced via circular motion of a Gaussian potential barrier stirring the condensate. We systematically explore a range of stirring parameters and identify three regimes, characterized by the injection of distinct quantum vortex structures into the condensate: (A) periodic vortex dipole injection, (B) irregular injection of a mixture of vortex dipoles and co-rotating vortex clusters, and (C) continuous injection of oblique solitons that decay into vortex dipoles. Spectral analysis of the kinetic energy associated with vortices reveals that regime (B) can intermittently exhibit a Kolmogorov ${k}^{\ensuremath{-}5/3}$ power law over almost a decade of length or wave-number (kkk) scales. The kinetic energy spectrum of regime (C) exhibits a clear ${k}^{\ensuremath{-}3/2}$ power law associated with an inertial range for weak-wave turbulence and a ${k}^{\ensuremath{-}7/2}$ power law for high wave numbers. We thus identify distinct regimes of forcing for generating either two-dimensional quantum turbulence or classical weak-wave turbulence that may be realizable experimentally.
Two-component fluids can be miscible (if they overlap in space) or immiscible (if they remain phase-separated). In the context of trapped two-species Bose-Einstein condensates (BECs), these miscibility regions can only be fully characterize if one considers the interspecies interaction, the mass ratio and the number of atoms in each species. The dynamics of coupled vortices is different for each miscibility region and exotic vortices configurations (such as, square vortex lattices, \\"vortex sheets\\", skyrmions, etc.) are expected to occur. In this thesis, we present the construction of a new experimental system able to produce a two-species Bose-Einstein condensate of 23Na-41K atoms with tunable interspecies interactions and study the dynamics of coupled vortices in the different miscibility regimes. The BEC of sodium atoms obtained first in a Plug trap and later, in a crossed optical dipole trap, is fully characterized as well as the cold atomic cloud of potassium atoms produced by means of a Gray molasses cooling procedure. In the crossed optical dipole trap, the vortices will be nucleated with the use of a stirring beam. Therefore, in the end of this thesis, we present the stirring beam setup and its characterization prior aligning it into the 23Na BEC.