Erratum: Creation and Detection of Skyrmions in a Bose-Einstein Condensate [Phys. Rev. Lett.103, 250401 (2009)]

Abstract

We report an error in the representation of the local spin, or ' vector, [Eq. (2)] of both the Skyrmion and half-Skyrmion in our Letter. We made the assumption that the three-component spin texture created in the F ¼ 2 manifold of 87 Rb and described by Eq. (1),was an effective spin-1 system composed of states: j2; 2i, j2; 0i, j2; À2i. It was further assumed that this pseudo-spin-1 system was equivalent to one consisting of spin states: j2; 1i, j2; 0i, j2; À1i.We presented the following ' vector for our spin textures:'ðrÞ ¼ẑ cosðrÞ þ sinðrÞðx cos' þŷ sin'Þ;where nðrÞ is the density of the cloud, (r, ') are polar coordinates, and ðrÞ is the bending angle. For the spin textures we created, Eq. (2) is only valid if both of the above assumptions hold. A full calculation of the expectation value of the local spin, h^Fi ¼', using the spin-2 order parameter of Eq. (1) and the spin-2 angular momentum spin matrices does not produce the ' vector of Eq. (2). As a result, the plots of the local spin, Figs. 1(e) and 2(e), are incorrect. All other representations of the data are based on the wave function, Eq. (1), and are still valid. In light of this error, it is not clear whether the classification of these spin textures as a Skyrmion and half-Skyrmion is still appropriate. PRL

Skyrmions in square-lattice antiferromagnets

“…Skyrmions have been the topic of intense research in ferromagnetic materials [1][2][3][4][5][6][7][8][9] as well as numerous other systems [10][11][12][13][14][15]. Skyrmions in ferromagnets have promising characteristics that make them suitable for data storage and transfer: They can be driven by low critical currents [16,17], and they are able to move past pinning sites [18].…”

Core Structure and Non-Abelian Reconnection of Defects in a Biaxial Nematic Spin-2 Bose-Einstein Condensate

“…Recent efforts in spin-1 BECs have led to the in situ observation of a singly quantized vortex splitting into a pair of HQVs [9], confirming theoretical prediction [8], and to controlled preparation of coreless-vortex textures [26][27][28], the analogs of Dirac [22] and 't Hooft-Polyakov [29] monopoles, and particlelike solitons [30]. Our results for spin-2 reveal a defect-structure phenomenology considerably richer than that in the spin-1 BECs [8,[31][32][33][34].…”

Angular spin-orbit coupling in cold atoms

“…To characterize the ground-state spin texture, we first define a normalized spin vector: Previous studies of 2D Rashba SO-coupled [23] BECs and BECs exposed to LG beams [19] have found that the spin texture contains a topological knot known as a 2D Skyrmion. Obtained from their 3D siblings by stereographic projection, 2D Skyrmions are a subject of interest in BEC studies for the protection that arises from their topological nontriviality.…”

“…Manipulating cold atoms with LG beams has been studied both experimentally and theoretically, in the context of quantum information storage [15], slow light propagation [16], synthetic gauge fields [17], etc. The experiments that directly motivated our investigations [18,19] used LG beams to diabatically write phase windings and spin textures into a BEC, producing coreless vortices and Skyrmions in the process. Our predictions are related to these results, though we focus on the adiabatic regime and consider the ground states of these systems.…”