Solitons in the discrete nonpolynomial Schrödinger equation

Maluckov, Aleksandra; Hadžievski, Ljupčo; Malomed, Boris A.; Salasnich, Luca

doi:10.1103/physreva.78.013616

Cited by 41 publications

(58 citation statements)

References 56 publications

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“…By solving Eq. (15) with CrankNicolson predictor-corrector algorithm with imaginary time [31] it is possible to show that in the attractive case (U < 0) discrete bright solitons exist [11].…”

Section: Numerical Resultsmentioning

confidence: 99%

“…Clearly, if U < 0 the transverse width σ i is smaller than one (i.e. σ i < a ⊥ in dimensional units) and the collapse happens when σ i goes to zero [11]. At the critical strength U c of the collapse all particles are accumulated in the two central sites (i = L/2 and i = L/2 + 1) around the minimum of the harmonic potential and consequently…”

Section: B Dimensional Reductionmentioning

confidence: 99%

“…To further simplify the problem we set (field-theory extension of the mean-field approach developed in [11])…”

Section: A Discretizationmentioning

confidence: 99%

“…Indeed, a negative s-wave scattering length implies an attractive interaction strength which may bring to the collapse [10,11] due to the shrink of the transverse width of a realistic quasi-1D bosonic cloud. Moreover in certain regimes of interaction the quasi-1D mean-field (MF) theory predicts the existence of meta-stable configurations [12] which are usually called discrete bright solitons.…”

Section: Introductionmentioning

confidence: 99%

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Quantum bright solitons in a quasi-one-dimensional optical lattice

Barbiero

Salasnich

2014

Phys. Rev. A

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We study a quasi-one-dimensional attractive Bose gas confined in an optical lattice with a super-imposed harmonic potential by analyzing the one-dimensional Bose-Hubbard Hamiltonian of the system. Starting from the three-dimensional many-body quantum Hamiltonian we derive strong inequalities involving the transverse degrees of freedom under which the one-dimensional Bose-Hubbard Hamiltonian can be safely used. In order to have a reliable description of the one-dimensional ground-state, that we call quantum bright soliton, we use the Density-MatrixRenormalization-Group (DMRG) technique. By comparing DMRG results with mean-field (MF) ones we find that beyond-mean-field effects become relevant by increasing the attraction between bosons or by decreasing the frequency of the harmonic confinement. In particular we find that, contrary to the MF predictions based on the discrete nonlinear Schrödinger equation, average density profiles of quantum bright solitons are not shape invariant. We also use the time-evolving-blockdecimation (TEBD) method to investigate dynamical properties of bright solitons when the frequency of the harmonic potential is suddenly increased. This quantum quench induces a breathing mode whose period crucially depends on the final strength of the super-imposed harmonic confinement.

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Section: Numerical Resultsmentioning

confidence: 99%

Section: B Dimensional Reductionmentioning

confidence: 99%

“…To further simplify the problem we set (field-theory extension of the mean-field approach developed in [11])…”

Section: A Discretizationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Quantum bright solitons in a quasi-one-dimensional optical lattice

Barbiero

Salasnich

2014

Phys. Rev. A

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“…The steady-state vortices were found numerically through the use of a nonlinear equation solver based on the Powell method 58 , whereas the vortex propagation was simulated using a sixth-order Runge-Kutta numerical procedure.…”

Section: Methodsmentioning

confidence: 99%

Stable optical vortices in nonlinear multicore fibers

et al. 2015

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The multicore fiber (MCF) is a physical system of high practical importance. In addition to standard exploitation, MCFs may support discrete vortices that carry orbital angular momentum suitable for spatial-division multiplexing in high-capacity fiber-optic communication systems. These discrete vortices may also be attractive for high-power laser applications. We present the conditions of existence, stability, and coherent propagation of such optical vortices for two practical MCF designs. Through optimization, we found stable discrete vortices that were capable of transferring high coherent power through the MCF. Keywords: coherent energy propagation; multicore fibers; nonlinear vortices INTRODUCTION Vortex structures are widespread in nature and are found in both macroscopic atmospheric phenomena, such as tornadoes and the Great Red Spot of Jupiter, and microscopic-scale objects in quantum physics. Mathematically, vortices are related to topological defects, the accumulation of geometrical phases, and the phase singularity of a complex linear or nonlinear field (see, e.g., Refs. 1-8 and references therein).Optical vortices present a fascinating and expanding area of research that combines fundamental theoretical and mathematical science and maturing applied technologies (see recent review 4 ). Optical vortices are characterized by a wave field with zero intensity, an undefined phase in the vortex center (pivot point) and the presence of a screw dislocation of the wave front 5,6 . All transmutations of vortices in linear and nonlinear fields obey the conservation of the topological charge S, which is defined as the total change of the phase along a closed curve surrounding the pivotal point of the vortex divided by 2p. The special behavior of the phase and amplitude near the vortex pivot point results in the circular flow of energy in optical vortices [7][8][9][10] . This property is closely related to the ability of optical vortices to carry orbital angular momentum and energy [11][12][13][14] . This property is interesting for various applications, such as in optical traps [15][16][17] , information transmission 18-20 , astrophysics 21,22 , microscopy 23,24 , and laser micromachining 25,26 .In nonlinear media, optical vortices are treated as (topological) vortex solitons 4,27,28 . Such topologically stable pulses can act as information carriers 4,[29][30][31] . It is important that continuum vortex solitons are highly sensitive to azimuthal instability. Stabilization is possible by applying optically induced photonic lattices, which lead to a discrete optical vortex field. Different types of discrete lattice vortex solitons were theoretically predicted in the Refs. 32-35 and experimentally demonstrated in the Refs. 36,37. Discrete vortex solitons can also be created in photonic crystal fibers and other types of photonic lattices 38,39 . Discrete vortex solitons are frequently associated with soliton clusters, which feature interesting mobility properties and

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Effective Equations for Repulsive Quasi‐One Dimensional Bose–Einstein Condensates Trapped with Anharmonic Transverse Potentials

2018

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One-dimensional nonlinear Schrödinger equations are derived to describe the axial effective dynamics of cigar-shaped atomic repulsive Bose-Einstein condensates trapped with anharmonic transverse potentials. The accuracy of these equations in the perturbative, Thomas-Fermi, and crossover regimes were verified numerically by comparing the ground-state profiles, transverse chemical potentials and oscillation patterns with those results obtained for the full three-dimensional Gross-Pitaevskii equation. This procedure allows us to derive different patterns of 1D nonlinear models by the control of the transverse confinement.

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Solitons in the discrete nonpolynomial Schrödinger equation

Cited by 41 publications

References 56 publications

Quantum bright solitons in a quasi-one-dimensional optical lattice

Quantum bright solitons in a quasi-one-dimensional optical lattice

Stable optical vortices in nonlinear multicore fibers

Effective Equations for Repulsive Quasi‐One Dimensional Bose–Einstein Condensates Trapped with Anharmonic Transverse Potentials

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