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arXiv:1207.1466 · Physical Review A

Vortices on demand in multicomponent Bose-Einstein condensates

Roberto Zamora-Zamora, M. Lozada-Hidalgo, Santiago F. Caballero-Benítez, Vı́ctor Romero-Rochı́n

Published Nov 26, 2012• 9 citations
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Abstract

We present a simple mechanism to produce vortices at any desired spatial locations in harmonically trapped Bose-Einstein condensates (BECs) 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 a 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.

DOI
10.1103/physreva.86.053624

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We present a simple mechanism to produce vortices at any desired spatial locations in harmonically trapped Bose-Einstein condensates (BECs) 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 a 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{}^{87}87Rb occupying all three F=1F=1F=1 states in an optical trap.
With use of the nonlinear Schr\"odinger (or Gross-Pitaevskii) equation with strong repulsive cubic nonlinearity, dynamics of multicomponent Bose-Einstein condensates (BECs) with a harmonic trap in two dimensions is investigated beyond the Thomas-Fermi regime. In the case when each component has a single vortex, we obtain an effective nonlinear dynamics for vortex cores (particles). The particles here acquire the inertia, in marked contrast to the standard theory of point vortices widely known in the usual hydrodynamics. The effective dynamics is equivalent to that of charged particles under a strong spring force and in the presence of Lorentz force with the uniform magnetic field. The interparticle (vortex-vortex) interaction is singularly repulsive and short ranged with its magnitude decreasing with increasing distance of the center of mass from the trapping center. ``Chaos in the three-body problem'' in the three-vortice system can be seen, which is not expected in the corresponding point vortices without inertia in two dimensions.
We study a square plaquette of four optical microtraps containing ultracold 87{}^{87}87Rb atoms in the F=1F=1F=1 hyperfine state. In the presence of an external resonant magnetic field, the dipolar interactions couple the initial mF=1{m}_{F}=1mF​=1 component to other Zeeman sublevels. This process is a generalization of the Einstein--de Haas effect to the case when the external potential has only C4{C}_{4}C4​ point symmetry. We observe that vortex structures appear in the initially empty mF=0{m}_{F}=0mF​=0 state. Topological properties of this state arise due to competition between the local axial symmetry of the individual trap and the discrete symmetry of the plaquette. For deep microtraps vortices are localized at individual sites, whereas for shallow traps only one discrete vortex appears in the plaquette. States created in these two opposite cases have different topological properties related to C4{C}_{4}C4​ point symmetry.
We study the stability of solitary vortices in a two-dimensional trapped Bose-Einstein condensate (BEC) with a spatially localized region of self-attraction. Solving the respective Bogoliubov--de Gennes equations and running direct simulations of the underlying Gross-Pitaevskii equation reveals that vortices with a topological charge up to S=6S=6S=6 (at least) are stable above a critical value of the chemical potential (i.e., below a critical number of atoms, which sharply increases with SSS). The largest nonlinearity-localization radius admitting stabilization of higher-order vortices is estimated analytically and accurately identified in numerical form. To the best of our knowledge, this is the first example of a setting which gives rise to stable higher-order vortices, S>1S>1S>1, in a trapped self-attractive BEC. The same setting may be realized in nonlinear optics too.
It is shown that a vortex can be continuously created in a Bose-Einstein condensate with hyperfine spin F=2 in a Ioffe-Pritchard trap by reversing the axial magnetic field adiabatically. It may be speculated that the condensate cannot be confined in the trap since the weak-field seeking state makes transitions to the neutral and the strong-field seeking states due to the degeneracy of these states along the vortex axis when the axial field vanishes. We have solved the Gross-Pitaevskii equation numerically with given external magnetic fields to show that this is not the case. It is shown that a considerable fraction of the condensate remains in the trap even when the axial field is reversed rather slowly. This scenario is also analysed in the presence of an optical plug along the vortex axis. Then the condensate remains within the Fz=2F_z=2Fz​=2 manifold, with respect to the local magnetic field, throughout the formation of a vortex and hence the loss of atoms does not take place.
We show that topological vortex pumping can be implemented for a dilute Bose-Einstein condensate confined in a magnetic time-averaged orbiting potential trap with axial optical confinement. Contrary to earlier proposals for the vortex pump, we do not employ an additional optical potential to trap the condensate in the radial direction, but instead, the radial confinement is provided by the magnetic field throughout the pumping cycle. By performing numerical simulations based on the spin-1 Gross-Pitaevskii equation, we find that several pumping cycles can be carried out to produce a highly charged vortex before a majority of the particles escape from the trap or before the vortex splits into singly charged vortices. On the other hand, we observe that an additional, relatively weak optical plug potential is efficient in preventing splitting and reducing particle loss. With these results, we hope to bring the vortex pump closer to experimental realization.
We numerically study the vortex-vortex interaction in multicomponent homogeneous Bose-Einstein condensates within the realm of the Gross-Pitaevskii theory. We provide strong evidence that pairwise vortex interaction captures the underlying mechanisms which determine the geometric configuration of the vortices, such as different lattices in many-vortex states, as well as the bound vortex states with two (dimer) or three (trimer) vortices. Specifically, we discuss and apply our theoretical approach to investigate intra- and intercomponent vortex-vortex interactions in two- and three-component Bose-Einstein condensates, thereby shedding light on the formation of the exotic vortex configurations. These results correlate with current experimental efforts in multicomponent Bose-Einstein condensates and the understanding of the role of vortex interactions in multiband superconductors.