Elastic collision and breather formation of spatiotemporal vortex light bullets in a cubic-quintic nonlinear medium

Adhikari, Sadhan K.

doi:10.1088/1612-202x/aa6c1c

Cited by 10 publications

(6 citation statements)

References 62 publications

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“…(93) below). Interactions between vortex solitons were investigated by means of direct simulations too [69,70]. Recent theoretical and experimental works with binary BEC have revealed a fascinating possibility of the creation of stable 3D and 2D soliton-shaped objects, which are stabilized by the LHY corrections to the mean-field (MF) theory, which account for the effect of quantum fluctuations around MF states [153].…”

Section: Interactions Between Multidimensional Solitonsmentioning

confidence: 99%

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(INVITED) Vortex solitons: Old results and new perspectives

Malomed

2019

Physica D: Nonlinear Phenomena

177

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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Section: Interactions Between Multidimensional Solitonsmentioning

confidence: 99%

“…( 93) below). Interactions between vortex solitons were investigated by means of direct simulations too [69,70].…”

Section: Interactions Between Multidimensional Solitonsmentioning

confidence: 99%

(INVITED) Vortex solitons: Old results and new perspectives

Malomed

2019

Physica D: Nonlinear Phenomena

177

115

View full text Add to dashboard Cite

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“…Apart from TG gas, quintic nonlinearity appears in a number of references. Recently, the formation of breathers through spatiotemporal vortex light bullets is discussed in a cubic-quintic nonlinear medium [37]. Oscillation of a dark soliton in a BEC with both cubic and quintic nonlinearities is observed, where the quintic nonlinearity in one dimension arises due to the interplay between the radial and axial degrees of freedom [38].…”

Section: Introductionmentioning

confidence: 99%

Lattice and quintic nonlinearity induced stripe phase in Bose–Einstein condensate under non-inertial and inertial motion

Das

2018

J. Phys. Commun.

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We consider a parametrically forced Bose-Einstein condensate in the combined presence of an optical lattice and harmonic oscillator potential in the mean field approach. A spatial symmetry broken Bosecondensed phase in non-inertial and inertial frame yields a stripe phase in the presence of both cubic and quintic nonlinearities. We show that the existence of such stripe phase solely depends on the interplay between the quintic nonlinearity and the lattice potential. Furthermore, we observe that a time-dependent harmonic oscillator frequency destroys such stripe ordering. A linear stability analysis of the obtained solution is performed and we found that the solution is stable. In order to gain a better understanding of the underlying physics, we compute the energy, showing nonlinear compression of the condensate in some parameter domain.

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“…The 3D quantum ball is stabilized in the presence of a repulsive three-body interaction and an adequate two-body attraction above a critical value [26][27][28] . It has been demonstrated that a tiny three-body repulsion stops the collapse and can stabilize a 3D quantum ball for zero 26 and non-zero angular momenta 29 . This gives the unique opportunity to study SSB in a 3D quantum ball bound solely by non-linear interactions placed in these parity-symmetric 1D potentials.…”

Section: Introductionmentioning

confidence: 99%

“…The mathematical structure of the non-linear mean-field GP equation is the same as that of the NLS equation used to study pulse propagation in non-linear optics, although the physical meaning of the different terms is distinct in two cases. Hence, in a cubic-quintic non-linear medium [30][31][32] one can have a stable mobile 3D spatiotemporal light bullet 28,29 and a SSB can occur in that context also.…”

Section: Introductionmentioning

confidence: 99%

Symmetry breaking, Josephson oscillation and self-trapping in a self-bound three-dimensional quantum ball

Adhikari

2017

Sci Rep

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We study spontaneous symmetry breaking (SSB), Josephson oscillation, and self-trapping in a stable, mobile, three-dimensional matter-wave spherical quantum ball self-bound by attractive two-body and repulsive three-body interactions. The SSB is realized by a parity-symmetric (a) one-dimensional (1D) double-well potential or (b) a 1D Gaussian potential, both along the z axis and no potential along the x and y axes. In the presence of each of these potentials, the symmetric ground state dynamically evolves into a doubly-degenerate SSB ground state. If the SSB ground state in the double well, predominantly located in the first well (z > 0), is given a small displacement, the quantum ball oscillates with a self-trapping in the first well. For a medium displacement one encounters an asymmetric Josephson oscillation. The asymmetric oscillation is a consequence of SSB. The study is performed by a variational and a numerical solution of a non-linear mean-field model with 1D parity-symmetric perturbations.

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Elastic collision and breather formation of spatiotemporal vortex light bullets in a cubic-quintic nonlinear medium

Cited by 10 publications

References 62 publications

(INVITED) Vortex solitons: Old results and new perspectives

(INVITED) Vortex solitons: Old results and new perspectives

Lattice and quintic nonlinearity induced stripe phase in Bose–Einstein condensate under non-inertial and inertial motion

Symmetry breaking, Josephson oscillation and self-trapping in a self-bound three-dimensional quantum ball

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