Collision Dynamics and Rung Formation of non-Abelian Vortices

Kobayashi, Michikazu; Kawaguchi, Yuki; Nitta, Muneto; Ueda, Masahito

doi:10.1103/physrevlett.103.115301

Cited by 105 publications

(99 citation statements)

References 45 publications

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“…In atomic systems, the topological classification and dynamics of non-Abelian vortices have theoretically been studied in the cyclic phase of spin-2 [13][14][15][16] and in spin-3 BECs [17], though it remains uncertain whether any alkali-metal atoms exhibit the corresponding ground states. Consequently, any physical system where non-Abelian defects may be reliably studied is still lacking.…”

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confidence: 99%

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

Borgh

Ruostekoski

2016

Phys. Rev. Lett.

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We calculate the energetic structure of defect cores and propose controlled methods to imprint a nontrivially entangled vortex pair that undergoes non-Abelian vortex reconnection in a biaxial nematic spin-2 condensate. For a singular vortex, we find three superfluid cores in addition to depletion of the condensate density. These exhibit order parameter symmetries that are different from the discrete symmetry of the biaxial nematic phase, forming an interface between the defect and the bulk superfluid. We provide a detailed analysis of phase mixing in the resulting vortex cores and find an instability dependent upon the orientation of the order parameter. We further show that the spin-2 condensate is a promising system for observing spontaneous deformation of a point defect into an "Alice ring" that has so far avoided experimental detection.Topological defects and textures are ubiquitous across physical systems that seemingly have little in common [1], from liquid crystals [2] and superfluids [3] to cosmic strings [4]. They arise generically from symmetries of a ground state that is described by an order parameter [5]-a function parametrizing the set of physically distinguishable, energetically degenerate states. In the simple example of a scalar superfluid, the order parameter is the phase of the macroscopic wave function. More generally it may be a vector or tensor that is symmetric under particular transformations. In a uniaxial nematic (UN), the order parameter is cylindrically symmetric around a locally defined axis. It also exhibits a twofold discrete symmetry under reversal of the cylinder axis, which leads to half-quantum vortices (HQVs) in atomic spinor BoseEinstein condensates (BECs) [6][7][8][9] and superfluid liquid 3 He [10], and to π disclinations in liquid crystals [1,2]. In a biaxial nematic (BN), also the cylindrical symmetry is broken into the fully discrete symmetry of a rectangular brick, with dramatic consequences: the BN is the simplest order parameter that supports non-Abelian vortices that do not commute [5,11]. As a result, colliding non-Abelian vortices cannot reconnect without leaving traces of the process, but must instead form a connecting rung vortex. Noncommuting defects appear as cosmic strings in theories of the early universe [4], and have been predicted in BN liquid crystals [11].Despite long-standing experimental efforts, BN phases in liquid crystals have experimentally proved more elusive than originally anticipated [12]. In atomic systems, the topological classification and dynamics of non-Abelian vortices have theoretically been studied in the cyclic phase of spin-2 [13-16] and in spin-3 BECs [17], though it remains uncertain whether any alkali-metal atoms exhibit the corresponding ground states. Consequently, any physical system where non-Abelian defects may be reliably studied is still lacking.Spin-2 BECs exhibit-in addition to the ferromagnetic (FM) and cyclic phases-both UN and BN phases [18][19][20], which, however, are degenerate at the mean-field level. Beyond mean-fi...

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confidence: 99%

“…They must instead reconnect by forming a rung vortex connecting the resulting defects. Non-Abelian defects have been proposed in BN liquid crystals [11] and theoretically classified in cyclic spin-2 BECs [13][14][15][16]48] and in certain spin-3 phases [17].…”

mentioning

confidence: 99%

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

Borgh

Ruostekoski

2016

Phys. Rev. Lett.

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“…The outer region then approaches the singly quantized vortex (24), exhibiting a radial disgyration ofd. In the limit of weak magnetization, the vortex core splits into two half-quantum vortices, similarly to the splitting of a singly quantized vortex predicted when magnetization is not conserved [26] and observed in experiment [5].…”

Section: Polar Regimementioning

confidence: 99%

“…We then explain how conservation of magnetization can also energetically stabilize the coreless vortex when it is phase imprinted on a BEC in the polar regime [34]. Equation (24) will then allow us to understand the stable coreless vortex as the composite core of a singly quantized vortex in the polar BEC. We also investigate whether conservation of magnetization can stabilize a nematic coreless vortex and explain our finding [34] that stability is achieved only at strong magnetization in an effective two-component regime.…”

Section: Nonsingular Vortices and Texturesmentioning

confidence: 99%

Stability and internal structure of vortices in spin-1 Bose-Einstein condensates with conserved magnetization

2016

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We demonstrate how conservation of longitudinal magnetization can have pronounced effects on both stability and structure of vortices in the atomic spin-1 Bose-Einstein condensate by providing a systematic characterization of nonsingular and singular vortex states. Constructing spinor wave functions for vortex states that continuously connect ferromagnetic and polar phases, we systematically derive analytic models for nonrotating cores of different singular vortices and for composite defect states with distinct small-and large-distance topology. We explain how the conservation law provides a stabilizing mechanism when the coreless vortex imprinted on the condensate relaxes in the polar regime of interatomic interactions. The resulting structure forms a composite defect: The inner ferromagnetic coreless vortex deforms toward an outer singly quantized polar vortex. We also numerically show how other even more complex hierarchies of vortex-core topologies may be stabilized. Moreover, we analyze the structure of the coreless vortex also in a ferromagnetic condensate and show how reducing magnetization leads to a displacement of the vortex from the trap center and eventually to the deformation and splitting of its core where a singular vortex becomes a lower-energy state. For the case of singular vortices, we find that the stability and the core structure are notably less influenced by the conservation of magnetization.

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“…This is because the spin and gauge degrees of freedom are coupled in a nontrivial manner. Examples include half-quantum vortices in the spin-1 polar phase [13] and 1/3-quantum vortices in the spin-2 cyclic phase [14][15][16].…”

Section: Introductionmentioning

confidence: 99%

Topological classification of vortex-core structures of spin-1 Bose-Einstein condensates

et al. 2012

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We classify vortex-core structures according to the topology of the order parameter space. We develop a method to characterize how the order parameter changes inside the vortex core. We apply it to spin-1 Bose-Einstein condensates and show that the vortex-core structures are classified by winding numbers that are locally defined in the core region. We also show that a vortex-core structure with a nontrivial winding number can be stabilized under a negative quadratic Zeeman effect.

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Collision Dynamics and Rung Formation of non-Abelian Vortices

Cited by 105 publications

References 45 publications

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

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

Stability and internal structure of vortices in spin-1 Bose-Einstein condensates with conserved magnetization

Topological classification of vortex-core structures of spin-1 Bose-Einstein condensates

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