Optical Solitons Carrying Orbital Angular Momentum

Firth, W. J.; Skryabin, Dmitry V.

doi:10.1103/physrevlett.79.2450

Cited by 336 publications

(238 citation statements)

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“…We will show that quantum vortices and their radially excited states can be made robustly stable in confined, attractive 2D condensates and are a generalization of the Townes soliton [20] to nonzero winding number m. The Townes soliton is fundamental to understanding the self-similar collapse of solutions to the 2D NLSE [21]. Its generalization to winding number |m| ≥ 1 has been studied in the context of optics, where such solutions are called "ring-profile solitary waves" or "spinning bright solitons" [22]. This is in fact the attractive analog of the well-known single vortex solution in repulsive condensates [2], as we will show.…”

Section: Pacs Numbersmentioning

confidence: 99%

Vortices in Attractive Bose-Einstein Condensates in Two Dimensions

Carr

Clark

2006

Phys. Rev. Lett.

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The form and stability of quantum vortices in Bose-Einstein condensates with attractive atomic interactions is elucidated. They appear as ring bright solitons, and are a generalization of the Townes soliton to nonzero winding number m. An infinite sequence of radially excited stationary states appear for each value of m, which are characterized by concentric matter-wave rings separated by nodes, in contrast to repulsive condensates, where no such set of states exists. It is shown that robustly stable as well as unstable regimes may be achieved in confined geometries, thereby suggesting that vortices and their radial excited states can be observed in experiments on attractive condensates in two dimensions.

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Section: Pacs Numbersmentioning

confidence: 99%

Vortices in Attractive Bose-Einstein Condensates in Two Dimensions

Carr

Clark

2006

Phys. Rev. Lett.

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“…On the other hand, vortex solitons are completely unstable against eigenmodes (B3) of azimuthal perturbations, with J = 1 and 2 for the vortices with m = 1, and J ≤ 4 for m = 2, similar to the instability of vortex solitons in the uniform χ (2) medium, which was studied in detail theoretically [31] and demonstrated experimentally [32]. However, direct simulations of Eqs.…”

Section: B Numerical Results For 2d Solitons and Vorticesmentioning

confidence: 99%

One- and two-dimensional solitons supported by singular modulation of quadratic nonlinearity

Lutsky

Malomed

2015

Phys. Rev. A

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We introduce a model of one-and two-dimensional (1D and 2D) optical media with the χ (2) nonlinearity whose local strength is subject to cusp-shaped spatial modulation, χ (2) ∼ r −α , with α > 0, which can be induced by spatially nonuniform poling. Using analytical and numerical methods, we demonstrate that this setting supports 1D and 2D fundamental solitons, at α < 1 and α < 2, respectively. The 1D solitons have a small instability region, while the 2D solitons have a stability region at α < 0.5 and are unstable at α > 0.5. 2D solitary vortices are found too. They are unstable, splitting into a set of fragments, which eventually merge into a single fundamental soliton pinned to the cusp. Spontaneous symmetry breaking of solitons is studied in the 1D system with a symmetric pair of the cusp-modulation peaks.

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“…Systematic simulations of the evolution of the VA families reveal an internal stability boundary, β st (S) < β max (S) (see Table 1), the vortices being stable at β < β st (S). In the interval of β st (S) < β < β max (0), they are broken by azimuthal perturbations into rotating necklace-shaped sets of fragments, which resembles the initial stage of the instability development of localized vortices in usual models [29,32,46,47]; however, unlike those models, the necklace does not expand, remaining confined under the action of the effective nonlocal interaction. Typical examples of the stable and unstable evolution of fundamental solitons and VAs are displayed, respectively, in Figs.…”

Section: The Resultsmentioning

confidence: 99%

Stable giant vortex annuli in microwave-coupled atomic condensates

2016

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Stable self-trapped vortex annuli (VAs) with large values of topological charge S (giant VAs) are not only a subject of fundamental interest, but are also sought for various applications, such as quantum information processing and storage. However, in conventional atomic Bose-Einstein condensates (BECs) VAs with S > 1 are unstable. Here, we demonstrate that robust self-trapped fundamental solitons (with S = 0) and bright VAs (with the stability checked up to S = 5), can be created in the free space by means of the local-field effect (the feedback of the BEC on the propagation of electromagnetic waves) in a condensate of two-level atoms coupled by a microwave (MW) field, as well as in a gas of MW-coupled fermions with spin 1/2. The fundamental solitons and VAs remain stable in the presence of an arbitrarily strong repulsive contact interaction (in that case, the solitons are constructed analytically by means of the Thomas-Fermi approximation). Under the action of the attractive contact interaction with strength β, which, by itself, would lead to collapse, the fundamental solitons and VAs exist and are stable, respectively, at β < β max (S) and β < β st (S), with β st (S = 0) = β max (S = 0) and β st (S ≥ 1) < β max (S ≥ 1). Accurate analytical approximations are found for both β st and β max , with β st (S) growing linearly with S. Thus, higher-order VAs are more robust than their lower-order couterparts, on the contrary to what is known in other systems that may support stable self-trapped vortices. Conditions for the experimental realizations of the VAs are discussed.

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Optical Solitons Carrying Orbital Angular Momentum

Cited by 336 publications

References 19 publications

Vortices in Attractive Bose-Einstein Condensates in Two Dimensions

Vortices in Attractive Bose-Einstein Condensates in Two Dimensions

One- and two-dimensional solitons supported by singular modulation of quadratic nonlinearity

Stable giant vortex annuli in microwave-coupled atomic condensates

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