Abstract
As a physical medium, cold atoms are wildly different from solid-state magnetic materials. Yet, some aspects of cold atom physics are subject to the same homotopy analysis we performed in Chap. 2, and relevant topological excitations can be classified accordingly. Indeed, vortices, skyrmions, and other interesting exotic topological excitations are possible states in spinor condensates, which are the quantum gases made up of atoms with spin.
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Notes
- 1.
Our derivation of the hydrodynamic action through a duality transformation follows from that of Kane and Lee [2].
- 2.
In the U(1) theory we used \(a_\mu \) instead of \(c_\mu \). Now, since \(a_\mu \) is used to express the CP\(^1\) gauge field, and \(b_\mu \) to express the emergent flux, the next available symbol is \(c_\mu \).
- 3.
The idea of a coreless vortex was originally proposed in the context of the A-phase of \(^3\)He and is known as the Anderson-Toulouse-Chechetkin vortex. Mathematically, this is just a two-dimensional skyrmion spin texture. Another kind of topological defect known as the Mermin-Ho vortex has half the winding number of the Anderson-Toulouse-Chechetkin vortex. Such spin structure is also known as the meron.
References
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Lee, D.H., Kane, C.L.: Boson-vortex-skyrmion duality, spin-singlet fractional quantum Hall effect, and spin-\({1\over 2}\) anyon superconductivity. Phys. Rev. Lett. 64, 1313 (1990)
Ho, T.L.: Spinor Bose condensates in optical traps. Phys. Rev. Lett. 81, 742 (1998)
Salomaa, M.M., Volovik, G.E.: Half-quantum vortices in superfluid \(^3\)He-A. Phys. Rev. Lett. 55, 1184 (1985)
Kawaguchi, Y., Ueda, M.: Spinor Bose-Einstein condensate. Phys. Rep. 520, 253 (2012)
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Han, J.H. (2017). Skyrmions in Spinor Bose-Einstein Condensates. In: Skyrmions in Condensed Matter. Springer Tracts in Modern Physics, vol 278. Springer, Cham. https://doi.org/10.1007/978-3-319-69246-3_8
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