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arXiv:2208.00807 · Journal of Experimental and Theoretical Physics Letters

Systems of Vortices in a Binary Core–Shell Bose–Einstein Condensate

V. P. Ruban

Published Sep 1, 2022• 5 citations
arXivHTMLPDF

Abstract

A trapped Bose–Einstein-condensed mixture of two types of cold atoms with significantly different masses has been simulated numerically within the coupled Gross–Pitaevskii equations. A configuration consisting of a vortex-free core and a shell penetrated by quantum vortices is possible in the phase separation regime. The dynamic properties of vortices in the shell are determined by several parameters. Physically implementable parametric domains corresponding to long-lived strongly nonstationary systems of several vortices attached to the core have been sought. A number of realistic numerical examples of three vortex pairs existing for many hundreds of characteristic times have been presented.

DOI
10.1134/s0021364022601579

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A trapped Bose–Einstein-condensed mixture of two types of cold atoms with significantly different masses has been simulated numerically within the coupled Gross–Pitaevskii equations. A configuration consisting of a vortex-free core and a shell penetrated by quantum vortices is possible in the phase separation regime. The dynamic properties of vortices in the shell are determined by several parameters. Physically implementable parametric domains corresponding to long-lived strongly nonstationary systems of several vortices attached to the core have been sought. A number of realistic numerical examples of three vortex pairs existing for many hundreds of characteristic times have been presented.
Abstract Specific topological excitations of energetically stable “core-and-mantle” configurations of trapped two-component immiscible Bose–Einstein condensates are studied numerically within the coupled Gross–Pitaevskii equations. Nonstationary long-lived coherent structures, that consist of several quantum vortex filaments penetrating the “mantle” from outside to inside and vice versa and demonstrate quite nontrivial dynamics, are observed in simulations for the first time. The ends of filaments can remain attached to the interface between the “mantle” and the “core” if the latter is large enough while the surface tension is not small. The shapes of such “bubbles” are strongly affected by the vortices and sometimes are far from being spherical.
There are many efforts to understand better the dipolar long-range interaction, the shell potential confinement, and the vortices in Bose-Einstein condensates (BECs). Furthermore, combining these three areas suggests that it can give rise to new phenomena. In this thesis, we studied the dynamics of vortices in a shell-trapped dipolar BEC. The long-range dipolar interaction induces an inhomogeneous density distribution on the shell, affecting the vortex velocity field. We analyzed the dynamics of one and two pairs of vortices symmetrically located in the shell to separate the vortex-vortex interaction contribution from that of the density gradient due to the inhomogeneous background. In addition to the numerical studies, a Lagrangian formalism allowed us to derive semi-analytical expressions which are in agreement with the results of the Gross-Pitaevskii equation (GPE) simulations, giving us better insights into the influence of the core in the vortex dynamics outside the validity of the point-vortex model. In the second part of this thesis, we describe an actual experimental implementation of the shell BEC. Using the Stochastic Projected GPE simulations, we determine the configuration of a finite temperature vortex lattice produced in this potential over the action of gravity. More specifically, we studied the transition from a perfectly hexagonal (triangular) lattice to the hexatic and liquid phases by detecting the vortex positions to calculate the angular and pair correlation functions of this system for different values of temperatures and trap rotation frequencies. Our results for the vortex lattice melting are consistent with the hexatic to liquid transition in the Kosterlitz-Thouless-Halperin-Nelson-Young (KTHNY) scenario and can be extended to predict the melting temperature of other finite-size systems.
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.
The properties of vortex states in a Bose-Einstein-condensed cloud of atoms are considered at zero temperature. Using both analytical and numerical methods, we solve the time-dependent Gross-Pitaevskii equation for the case when a cloud of atoms containing a vortex is released from a trap. In two dimensions we find the simple result that the time dependence of the cloud radius is given by $(1+{\ensuremath{\omega}}^{2}{t}^{2}{)}^{1/2},$ where $\ensuremath{\omega}$ is the trap frequency. We calculate and compare the expansion of the vortex core and the cloud radius for different numbers of particles and interaction strengths, in both two and three dimensions, and discuss the circumstances under which vortex states may be observed experimentally.
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.
In this work, we consider vortex lattices in rotating Bose–Einstein condensates composed of two species of bosons having different masses. Previously (Barnett et al 2008 New J. Phys. 10 043030), it was claimed that the vortices of the two species form bound pairs and the two vortex lattices lock. Remarkably, the two condensates and the external drive all rotate at different speeds owing to the disparity of the masses of the constituent bosons. In this paper, we study the system by solving the full two-component Gross–Pitaevskii equations numerically. Using this approach, we verify the stability of the putative locked state that is found to exist within a disc centered on the axis of rotation and that depends on the mass ratio of the two bosons. We also derive a refined estimate for the locking radius tailored to the experimentally relevant case of a harmonic trap and show that this agrees with the numerical results. Finally, we analyze in detail the rotation rates of the different components in the locked and unlocked regimes.