Nonlinear phenomena in degenerate quantum gases

Pérez-Garcı́a, Vı́ctor M.; Berloff, Natalia G.; Kevrekidis, P. G.; Malomed, Boris A.

doi:10.1016/j.physd.2009.05.001

Cited by 14 publications

(10 citation statements)

References 226 publications

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“…Theoretical and experimental studies of solitons have grown into a huge research area penetrating many disciplines, in physics, mathematics, and beyond. The largest share of these works have been dealing with one-dimensional (1D) solitons [2,3], the dominant areas in current studies of solitons being nonlinear optics [2] and Bose-Einstein condensates (BECs) in ultracold atomic gases [5][6][7][8][9][10]. The extension of the concept of solitons to two-and three-dimensional (2D and 3D) geometry is a highly nontrivial generalization (multidimensional optical solitons, which are self-trapped (localized) both in the spatial and temporal directions, are often called spatiotemporal solitons [11], alias "light bullets" [4]).…”

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confidence: 99%

(INVITED) Vortex solitons: Old results and new perspectives

Malomed

2019

Physica D: Nonlinear Phenomena

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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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(INVITED) Vortex solitons: Old results and new perspectives

Malomed

2019

Physica D: Nonlinear Phenomena

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177

115

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“…The balance of dispersion and nonlinear interactions in BECs leads to different types of nonlinear coherent excitations (see, e.g., the experimental papers [2][3][4][5][6][7][8] or the reviews [9,10]). Soliton molecules have been considered in the propagation of optical beams in nonlinear media with saturable nonlinearities [11][12][13][14], it being very difficult to construct even metastable long-living soliton clusters with local interactions such as those present in ordinary BECs.…”

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Coherent atomic soliton molecules for matter-wave switching

et al. 2011

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We discuss the dynamics of interacting dark-bright two-dimensional vector solitons in multicomponent immiscible bulk Bose-Einstein condensates. We describe matter-wave molecules without a scalar counterpart that can be seen as bound states of vector objects. We also analyze the possibility of using these structures as building blocks for the design of matter-wave switchers.Comment: 4 pages, 5 figure

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“…In the case when all the functions depend only on ξ = x − u 0 t integrating the continuity equation (6)…”

Section: Motion With Stationary-profile Current Velocitymentioning

confidence: 99%

“…The previous discussion is easily extended to the situation when two waves have normal dispersion and one is anomalous, corresponding to one bright-two dark solitons interaction. Such vector solitons of mixed bright-dark types are of interest in quasi-one-dimensional Bose-Einstein condensates (see [6] and references therein). We are interested in a SW-LW resonance regime, so several restrictions on the model of three interacting waves will be imposed.…”

Section: One Bright-two Dark Solitons Interactionmentioning

confidence: 99%

“…In particular, to describe the propagation of three nonlinear pulses in some dispersive material one has to solve simultaneously a set of coupled nonlinear Schrödinger (NLS) equations. For instance, it occurs in: (i) the propagation of solitonlike pulses in birefringent optical fibers [1,2,3,4]; (ii) the nonlinear wave dynamics of Bose-Einstein condensates [5,6]; (iii) the soliton propagation through optical fiber array [1,7,8,9]; (iv) the nonlinear dynamics of gravity waves in crossing sea states [10].…”

Section: Introductionmentioning

confidence: 99%

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Periodic and Solitary Wave Solutions of Two Component Zakharov-Yajima-Oikawa System, Using Madelung's Approach

Vişinescu¹

2011

SIGMA

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Abstract. Using the multiple scales method, the interaction between two bright and one dark solitons is studied. Provided that a long wave-short wave resonance condition is satisfied, the two-component Zakharov-Yajima-Oikawa (ZYO) completely integrable system is obtained. By using a Madelung fluid description, the one-soliton solutions of the corresponding ZYO system are determined. Furthermore, a discussion on the interaction between one bright and two dark solitons is presented. In particular, this problem is reduced to solve a one-component ZYO system in the resonance conditions.

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Nonlinear phenomena in degenerate quantum gases

Cited by 14 publications

References 226 publications

(INVITED) Vortex solitons: Old results and new perspectives

(INVITED) Vortex solitons: Old results and new perspectives

Coherent atomic soliton molecules for matter-wave switching

Periodic and Solitary Wave Solutions of Two Component Zakharov-Yajima-Oikawa System, Using Madelung's Approach

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