Linked and knotted synthetic magnetic fields

Duncan, Callum W.; Ross, Calum; Westerberg, Niclas; Valiente, Manuel; Schroers, Bernd J.; Öhberg, Patrik

doi:10.1103/physreva.99.063613

Cited by 10 publications

(4 citation statements)

References 81 publications

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“…The other vortex topologies have also been generated in a specific superposition of beams, e.g. linked and knotted synthetic magnetic fields [65].…”

Section: Design Methodsmentioning

confidence: 99%

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Optical vortex knots and links via holographic metasurfaces

Guo

Zhong

Liu

et al. 2020

Advances in Physics: X

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Vortices arise in many natural phenomena as dark points of total destructive interference. Sometimes they form continuous lines and even enclosed loops with knotted or linked topologies in three spatial dimensions. Since the mathematical topology was introduced into physics, from hydrodynamics, condensed matter physics to photonics, and other modern physical fields, scientists have been exploring the related topological essences of vortex knots; hence, the topology is a forefront topic in different physical systems. Owing to the reliability and observability of light in free space, optical vortex knots and links are the most studied physical topologies. Here, we review some of these developments with a focus on optical vortex knots and links. We first introduce the brief historical perspective and structural properties of optical vortices. Then, we trace the progress on the theoretically constructing, experimentally generating, and characterizing methods of topological light fields. Wherein, we review recent developments of holographic metasurfaces and their applications in generating ultrasmall optical vortex knots. At last, we envision the possible challenges and prospects of topological light fields.

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“…The other vortex topologies have also been generated in a specific superposition of beams, e.g. linked and knotted synthetic magnetic fields [65].…”

Section: Design Methodsmentioning

confidence: 99%

“…This entanglement of photons in complex 3D topological states suggests the possibility of entanglement of similar features in other systems. In addition, the knotted fields can act as synthetic gauge fields on neutral atomic gas, and transfer the topological properties to the ground state of a 3D Bose-Einstein condensate [65].…”

Section: Applicationsmentioning

confidence: 99%

Optical vortex knots and links via holographic metasurfaces

Guo

Zhong

Liu

et al. 2020

Advances in Physics: X

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“…Time evolution of knotted fields. Questions about the time evolution of knots and links in physical systems that were constructed from complex-valued maps, such as quantum knots or in knots in magnetic fields have been raised in [21] and [14], respectively. At this stage it is not clear if and how the constructed polynomials from the previous sections can be used to create knotted configurations of physical systems in R 3 that evolve as desired.…”

Section: 3mentioning

confidence: 99%

Knotted surfaces as vanishing sets of polynomials

Bode

Kamada²

2020

Preprint

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We present an algorithm that takes as input any element B of the loop braid group and constructs a polynomial f : R 5 → R 2 such that the intersection of the vanishing set of f and the unit 4-sphere contains the closure of B. The polynomials can be used to create real analytic time-dependent vector fields with zero divergence and closed flow lines that move as prescribed by B. We also show how a family of surface braids in C × S 1 × S 1 without branch points can be constructed as the vanishing set of a holomorphic polynomialBoth constructions allow us to give upper bounds on the degree of the polynomials.

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“…This provides an important new tool for accessing some of the paradigmatic effects associated with condensed matter physics, including simulating orbital magnetism [34][35][36][37]. Ultracold atomic gases provide a platform for implementing not only these traditional manifestations of magnetism; but also for realizing forms of magnetism that are not naturally occurring, such as spin-orbit [38,39] and spin-angular momentum coupling [40,41] with bosons, synthetic dimensions [42], 'knotted' gauge theories [43] and density-dependent magnetism [44]. The realization of spin-orbit coupled bosons in-particular yields a new route to investigate the interplay of synthetic electromagnetism and rotation [45][46][47].…”

Section: Introductionmentioning

confidence: 99%

Vortex patterns of atomic Bose-Einstein condensates in a density-dependent gauge potential

Edmonds,

Nitta

2020

Preprint

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We theoretically examine the vortex states of a gas of trapped quasi-two-dimensional ultracold bosons subject to a density-dependent gauge potential, realizing an effective nonlinear rotation of the atomic condensate. The nonlinear rotation has a two-fold effect; as well as distorting the shape of the condensate it also leads to an inhomogeneous vorticity resulting in novel morphological and topological states, including ring vortex arrangements that do not follow the standard Abrikosov result. The dynamics of trapped vortices are also explored, which differs from the case of linear rotation due to the absence of a global laboratory reference frame.

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Linked and knotted synthetic magnetic fields

Cited by 10 publications

References 81 publications

Optical vortex knots and links via holographic metasurfaces

Optical vortex knots and links via holographic metasurfaces

Knotted surfaces as vanishing sets of polynomials

Vortex patterns of atomic Bose-Einstein condensates in a density-dependent gauge potential

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