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arXiv:cond-mat/0307721 · Physical Review A

Dirac monopoles and dipoles in ferromagnetic spinor Bose-Einstein condensates

Craig M. Savage, Janne Ruostekoski

Published Oct 6, 2003• 57 citations
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Abstract

We investigate a radial spin hedgehog, analogous to the Dirac monopole, in an optically trapped atomic spin-1 Bose-Einstein condensate. By joining together a monopole-antimonopole pair, we may form a vortex line with free ends. We numerically simulate the three-dimensional dynamics and imaginary time relaxation of these structures to nonsingular textures and show that they can be observable for realistic experimental parameters.

DOI
10.1103/physreva.68.043604

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We investigate a radial spin hedgehog, analogous to the Dirac monopole, in an optically trapped atomic spin-1 Bose-Einstein condensate. By joining together a monopole-antimonopole pair, we may form a vortex line with free ends. We numerically simulate the three-dimensional dynamics and imaginary time relaxation of these structures to nonsingular textures and show that they can be observable for realistic experimental parameters.
We theoretically demonstrate that a pair of Dirac monopoles with opposite synthetic charges can be created within a single spin-1 Bose-Einstein condensate by steering the spin degrees of freedom by external magnetic fields. Although the net synthetic magnetic charge of this configuration vanishes, both the monopole and the antimonopole are accompanied by vortex filaments carrying opposite angular momenta. Such a Dirac dipole can be realized experimentally by imprinting a spin texture with a nonlinear magnetic field generated by a pair of coils in a modified Helmholtz configuration. We also investigate the case where the initial state for the dipole-creation procedure is pierced by a quantized vortex line with a winding number $\ensuremath{\kappa}$. It is shown that if $\ensuremath{\kappa}=\ensuremath{-}1$, the resulting monopole and antimonopole lie along the core of a singly quantized vortex whose sign is reversed at the locations of the monopoles. For $\ensuremath{\kappa}=\ensuremath{-}2$, the monopole and antimonopole are connected by a vortex line segment carrying two quanta of angular momentum, and hence the dipole as a whole is an isolated configuration. In addition, we simulate the long-time evolution of the dipoles in the magnetic field used to create them. For $\ensuremath{\kappa}=0$, each of the semi-infinite doubly quantized vortices splits into two singly quantized vortices, as in the case of a single Dirac monopole. For $\ensuremath{\kappa}=\ensuremath{-}1$ and $\ensuremath{\kappa}=\ensuremath{-}2$, the initial vortices deform into a vortex with a kink and a vortex ring, respectively.
We show theoretically that a monopole defect, analogous to the Dirac magnetic monopole, may exist as the ground state of a dilute spin-1 Bose-Einstein condensate. The ground-state monopole is not attached to a single semi-infinite Dirac string but forms a point where the circulation of a single vortex line is reversed. Furthermore, the three-dimensional dynamics of this monopole defect is studied after the magnetic field pinning the monopole is removed and the emergence of antimonopoles is observed. Our scheme is realizable with the current experimental facilities.
We report Dirac monopoles with a polar-core vortex induced by spin-orbit coupling in ferromagnetic Bose-Einstein condensates, which are attached to two nodal vortex lines along the vertical axis. These monopoles are more stable in the time scale of experiment and can be detected through directly imaging vortex lines. When the strength of spin-orbit coupling increases, Dirac monopoles with a vortex can be transformed into those with a square lattice. In the presence of spin-orbit coupling, increasing the strength of the interaction can induce a cyclic phase transition from Dirac monopoles with a polar-core vortex to those with a Mermin-Ho vortex. The spin-orbit coupled Bose-Einstein condensates not only provide a unique platform for investigating exotic monopoles and relevant phase transitions but also can hold stable monopoles even though a quadrupole field is turned off.
We study numerically the detailed structure and decay dynamics of isolated monopoles in conditions similar to those of their recent experimental discovery. We find that the core of a monopole in the polar phase of a spin-1 Bose-Einstein condensate contains a small half-quantum vortex ring. Well after the creation of the monopole, we observe a dynamical quantum phase transition that destroys the polar phase. Strikingly, the resulting ferromagnetic order parameter exhibits a Dirac monopole in its synthetic magnetic field. We observe quantitatively matching decay dynamics for both ferromagnetic and antiferromagnetic spin-spin interactions.
Magnetic monopoles describe isolated north or south magnetic poles. The practical detection of the free magnetic monopoles, due to their extremely heavy masses, remains challenging so far. However, Bose-Einstein condensates offer an ideal observable platform for probing monopoles. In particular, the recent realization of spin-orbit (SO) coupling, owing to its high controllability and tunability, provides an unprecedented opportunity to explore exotic structures and phase transitions of monopoles unrealizable elsewhere. Here we report Dirac monopoles attached to the polar-core vortex induced by SO coupling in ferromagnetic Bose-Einstein condensates, which can be readily observed via time of flight measurements in experiment. The results show that, a cyclic phase transition from Dirac monopoles with polar-core vortex to that with Mermin-Ho vortex, is induced by SO coupling. Our studies may open a new direction to realize exotic topological defects and phase transitions in quantum systems.
We demonstrate theoretically that, by using external magnetic fields, one can imprint pointlike topological defects on the spin texture of a dilute Bose-Einstein condensate. The symmetries of the condensate order parameter render this topological defect to be accompanied with a vortex filament corresponding to the Dirac string of a magnetic monopole. The vorticity in the condensate coincides with the magnetic field of a magnetic monopole, providing an ideal analogue to the monopole studied by Dirac.