Rotating trapped Bose-Einstein condensates

Fetter, Alexander L.

doi:10.1134/s1054660x08010015

Cited by 107 publications

(190 citation statements)

References 164 publications

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“…They are well-known objects, studied in detail theoretically and created in experiments, prior to the work on bright vortex solitons. Results obtained for the "dark vortices", starting from the earliest ones [86][87][88], have been collected in many publications dealing with various settings in photonics [89][90][91][92][93][94][95] (including exciton-polariton condensates [96][97][98], where the vortices exist in dissipative media) and BEC [61,[99][100][101][102][103][104][105], as well as in quantum Fermi gases [106,107]; see also book [108] for an overview of the theme. The studies of vortices in this context are also known as "singular optics", with pivots of the vortices considered as singularities of optical fields; many publications on the latter theme were collected in a special issue of Journal of Optics [109] (see also book [110]).…”

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confidence: 99%

(INVITED) Vortex solitons: Old results and new perspectives

Malomed

2019

Physica D: Nonlinear Phenomena

176

115

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A comparative review is given of some well-known and some recent results obtained in studies of two-and three-dimensional (2D and 3D) solitons, with emphasis on states carrying embedded vorticity. Physical realizations of multidimensional solitons in atomic Bose-Einstein condensates (BECs) and nonlinear optics are briefly discussed too. Unlike 1D solitons, which are typically stable, 2D and 3D ones are vulnerable to instabilities induced by the occurrence of the critical and supercritical collapse, respectively, in the 2D and 3D models with the cubic self-focusing nonlinearity. Vortex solitons are subject to a still stronger splitting instability. For this reason, a central problem is looking for physical settings in which 2D and 3D solitons may be stabilized. The review addresses in detail two well-established topics, viz., the stabilization of vortex solitons by means of competing nonlinearities, or by trapping potentials (harmonic-oscillator and spatially-periodic ones). The former topic includes a new addition, closely related to the recent breakthrough, viz., the prediction and creation of robust quantum droplets. Two other topics included in the review outline new schemes which were recently elaborated for the creation of stable vortical solitons in BEC. One scheme relies on the use of the spin-orbit coupling (SOC) in binary condensates with cubic intrinsic attraction, making it possible to predict stable 2D and 3D solitons, which couple or mix components with vorticities S = 0 and ±1 (semi-vortices (SVs) or mixed modes (MMs), respectively). In this system, the situation is drastically different in the 2D and 3D geometries. In 2D, the SOC helps to create a ground state (GS, which does not exist otherwise), represented by stable SV or MM solitons, whose norm falls below the threshold value at which the critical collapse sets in. In the 3D geometry, the supercritical collapse does not allow one to create a GS, but metastable solitons of the SV and MM types can be constructed. Another new scheme makes it possible to create stable 2D vortex-ring solitons with arbitrarily high S in a binary BEC with components coupled by microwave radiation. Some other topics are addressed briefly, such as vortex solitons in dissipative media, and attempts to create vortex solitons in experiments.List of acronyms: 1D -one-dimensional; 2D -two dimensional; 3D -three-dimensional; BEC -Bose-Einstein condensate; CGLE -complex Ginzburg-Landau equation; CQ -cubic-quintic (nonlinearity), FF -fundamental frequency; GPE -Gross-Pitaevskii equation; GS -ground state; GVD -group-velocity dispersion; HO -harmonic oscillator (potential); HV -hidden vorticity; LHY -Lee-Huang-Yang (correction to the mean-field dynamics of BEC); MF -mean field; MM -mixed mode; NLSE -nonlinear Schrödinger equation; OL -optical lattice; PT -parity-time (symmetry); QD -quantum droplet; SH -second harmonic; SOC -spin-orbit coupling; SV -semi-vortex; TF -Thomas-Fermi (approximation); TS -Townes' soliton; VA -variational approximation; VAV -vortex-antivortex (composit...

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confidence: 99%

(INVITED) Vortex solitons: Old results and new perspectives

Malomed

2019

Physica D: Nonlinear Phenomena

176

115

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“…The GP equation and its vortex solutions is a subject of its own that can be studied independently of the many-body problem. See the monograph [13] and the review article [14] where a large number of references can be found. The most detailed results are for the two-dimensional GP equation, i.e.…”

Section: The General Settingmentioning

confidence: 99%

“…is no longer bounded below [28], see also [14] for a review. As Ω c − Ω → 0 + the effective radius R of the condensate tends to infinity and the system becomes effectively two-dimensional.…”

Section: Remarks On Rapid Rotation In Harmonic Trapsmentioning

confidence: 99%

Bosons in Rapid Rotation

Yngvason

2008

Int. J. Geom. Methods Mod. Phys.

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“…A major research track within this broad theme concerns the nonlinear properties of the solitary waves supported by the weakly interacting gas, sharing many similarities with nonlinear optics [3]. In this context, a large variety of solitary waves has been studied in the context of BECs, ranging from dark solitons [4], vortices and vortex lines [5,6], vortex rings [7] to more complex vortical structures such as long-lived knots [8]. On the other hand, the creation of fermionic and multicomponent condensates is believed to be useful for understanding the high-temperature superconductivity [9].…”

Section: Introductionmentioning

confidence: 99%

Ring dark solitons in three-dimensional Bose-Einstein condensates

2019

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In this work we present a systematic study of the three-dimensional extension of the ring dark soliton examining its existence, stability, and dynamics in isotropic harmonically trapped Bose-Einstein condensates. Detuning the chemical potential from the linear limit, the ring dark soliton becomes unstable immediately, but can be fully stabilized by an external cylindrical potential. The ring has a large number of unstable modes which are analyzed through spectral stability analysis. Furthermore, a few typical destabilization dynamical scenarios are revealed with a number of interesting vortical structures emerging such as the two or four coaxial parallel vortex rings. In the process of considering the stability of the structure, we also develop a modified version of the degenerate perturbation theory method for characterizing the spectra of the coherent structure. This semianalytical method can be reliably applied to any soliton with a linear limit to explore its spectral properties near this limit. The good agreement of the resulting spectrum is illustrated via a comparison with the full numerical Bogolyubov-de Gennes spectrum. The application of the method to the two-component ring dark-bright soliton is also discussed. * Electronic address: wenlongcmp@gmail.com † Electronic address: kevrekid@math.umass.edu FIG. 1: Density contour and phase profile of a stationary ring dark soliton in a spherical harmonic trap of frequency ω = 1 at chemical potential µ = 16 (Eq. (1)). There is a ring of vanishing density separating two segments with phase difference of π shown as two different colours (red and green). Note the ring is not vertically straight, but bends. The state is generated from numerical computation. the incongruence between the cylindrical symmetry of the 2D pattern and the closer to spherical (or more accurately: ellipsoidal) nature of the 3D condensate. A cross section perpendicular to the axis is a 2D ring, and the radius is larger at the edges and smaller at the center. See Fig. 1 for a density and phase profile of the RDS.Despite its extensive analysis in the 2D case, including the recent corroboration of its modes of vibration and even its multi-component extension [18], the RDS has not been studied in detail in three dimensions. Instead, other structures, such as the planar dark soliton (PDS) [19,20] and the spherical dark soliton (SDS) [20,21] have been considered due to their symmetry. The latter have been dynamically recognized as generating spontaneously structures such as vortex rings and multi-ring generalizations thereof [19,22,23]. In that arXiv:1910.02272v1 [cond-mat.quant-gas]

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Rotating trapped Bose-Einstein condensates

Cited by 107 publications

References 164 publications

(INVITED) Vortex solitons: Old results and new perspectives

(INVITED) Vortex solitons: Old results and new perspectives

Bosons in Rapid Rotation

Ring dark solitons in three-dimensional Bose-Einstein condensates

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