We address the properties of optical solitons in thermal nonlinear media with a local refractive index defect that is capable to trap solitons launched even close to the sample boundary despite the boundary-mediated forces that tend to deflect all beams toward the center of the sample. We show that while such forces become more pronounced with increasing the input beam power the defect can trap only light below a critical power above which solitons are ejected. The dynamics of soliton ejection and the subsequent propagation may be controlled.
We show that self-localized ground states can be created in the spin-balanced gas of fermions with repulsion between the spin components, whose strength grows from the center to periphery, in combination with the harmonic-oscillator (HO) trapping potential acting in one or two transverse directions. We also consider the ground state in the non-interacting Fermi gas under the action of the spatially growing tightness of the one- or two-dimensional (1D or 2D) HO confinement. These settings are considered in the framework of the Thomas-Fermi-von Weizsacker (TF-vW) density functional. It is found …
We explore the fundamental question of the critical nonlinearity value needed to dynamically localize energy in discrete nonlinear cubic (Kerr) lattices. We focus on the effective frequency and participation ratio of the profile to determine the transition into localization in one-, two-, and three-dimensional lattices. A simple and general criterion is developed, for the case of an initially localized excitation, to define the transition region in parameter space ("dynamical tongue") from a delocalized to a localized profile. We introduce a method for computing the dynamically excited frequen…
We elaborate a method for the creation of two- and one-dimensional (2D and 1D) self-trapped modes in binary spin-orbit (SO)-coupled Bose-Einstein condensates (BECs) with the contact repulsive interaction, whose local strength grows fast enough from the center to periphery. In particular, an exact semi-vortex (SV) solution is found for the anti-Gaussian radial-modulation profile. The exact modes are included in the numerically produced family of SV solitons. Other families, in the form of mixed modes(MMs), as well as excited state of SVs and MMs, are produced too. While the excited states are u…
We demonstrate that the fission of higher-order N-solitons with a subsequent ejection of fundamental quasi-solitons creates solitonic cavities, formed by a pair of solitons with dispersive light trapped between them. As a result of multiple reflections of the trapped light from the bounding solitons which act as mirrors, they bend their trajectories and collide. In the spectral-domain, the two solitons receive blue and red wavelength shifts, respectively. The spectrum of the bouncing trapped light alters as well. This phenomenon strongly affect spectral characteristics of the generated superco…
We show that bimodal systems with a spatially nonuniform defocusing cubic nonlinearity, whose strength grows toward the periphery, can support stable two-component solitons. For a sufficiently strong XPM interaction, vector solitons with overlapping components become unstable, while stable families of solitons with spatially separated components emerge. Stable complexes with separated components may be composed not only of fundamental solitons, but of multipoles too.
We investigate competition between two phase transitions of the second kind induced by the self-attractive nonlinearity, viz., self-trapping of the leaky modes, and spontaneous symmetry breaking (SSB) of both fully trapped and leaky states. We use a one-dimensional mean-field model, which combines the cubic nonlinearity and a double-well-potential (DWP) structure with an elevated floor, which supports leaky modes (quasi-bound states) in the linear limit. The setting can be implemented in nonlinear optics and BEC. The order in which the SSB and self-trapping transitions take place with the grow…
We consider a microcavity made by a graded-index (GRIN) glass, doped by dye molecules, placed within two planar mirrors and study Bose-Einstein condensation (BEC) of photons. The presence of the mirrors leads to an effective photon mass, and the index grading provides an effective trapping frequency; the photon gas becomes formally equivalent to a two dimensional Bose gas trapped in an isotropic harmonic potential. The inclusion of nonlinear effects provides an effective interaction between photons. We discuss, in particular, thermal lensing effects and nonlocal nonlinearity, and quantitativel…
We address the existence and stability of localized modes in the framework of the fractional nonlinear Schroedinger equation (FNSE) with the focusing cubic or focusing-defocusing cubic-quintic nonlinearity and a confining harmonic-oscillator (HO) potential. Approximate analytical solutions are obtained in the form of Hermite-Gauss modes. The linear stability analysis and direct simulations reveal that, under the action of the cubic self-focusing, the single-peak ground state and dipole mode are stabilized by the HO potential at values of the Levy index (the fractionality degree) alpha = 1 and …
Observation of linear and nonlinear light trapping on topological dislocations
Universidad de Valencia（瓦伦西亚大学）；Institute of Spectroscopy, Russian Academy of Sciences（俄罗斯科学院光谱学研究所）；Moscow Institute of Physics and Technology (National Research University)（莫斯科物理技术学院（国立研究型大学））；Quantum Technology Centre, Faculty of Physics, M. V. Lomonosov Moscow State University（莫斯科罗蒙诺索夫国立大学物理学院量子技术中心）
The stationary solutions of the Gross-Pitaevskii equation can be divided in two classes: those which reduce, in the limit of vanishing nonlinearity, to the eigenfunctions of the associated Schrödinger equation and those which do not have linear counterpart. Analytical and numerical results support an existence condition for the solutions of the first class in terms of the ratio between their proper frequency and the corresponding linear eigenvalue. For one-dimensional confined systems, we show that solutions without linear counterpart do exist in presence of a multi-well external potential. Th…
We report on the first observation of surface gap solitons, recently predicted to exist at the interface between uniform and periodic dielectric media with defocusing nonlinearity [Ya.V. Kartashov et al., Phys. Rev. Lett. 96, 073901 (2006). We demonstrate strong self-trapping at the edge of a LiNbO_3 waveguide array and the formation of staggered surface solitons with propagation constant inside the first photonic band gap. We study the crossover between linear repulsion and nonlinear attraction at the surface, revealing the mechanism of nonlinearity-mediated stabilization of the surface gap m…
Solitons are typically stable objects in 1D models, but their straightforward extensions to 2D and 3D settings tend to be unstable. In particular, the ubiquitous nonlinear Schroedinger (NLS) equation with the cubic self-focusing, creates only unstable 2D and 3D solitons, because the same equation gives rise to the critical and supercritical collapse in the 2D and 3D cases, respectively. This article offers, first, a review of relevant settings which, nevertheless, make it possible to create stable 2D and 3D solitons, including ones with embedded vorticity. The main stabilization schemes consid…
We find that the recently introduced model of self-trapping supported by a spatially growing strength of a repulsive nonlinearity gives rise to robust vortex-soliton tori, i.e., three-dimensional vortex solitons, with topological charges S. The family with S=1 is completely stable, while the one with S=2 has alternating regions of stability and instability. The families are nearly exactly reproduced in an analytical form by the Thomas-Fermi approximation (TFA). Unstable states with S=2 and 3 split into persistently rotating pairs or triangles of unitary vortices. Application of a moderate torq…
We present eight types of spatial optical solitons which are possible in a model of a planar waveguide that includes a dual-channel trapping structure and competing (cubic-quintic) nonlinearity. Among the families of trapped beams are symmetric and antisymmetric solitons of "broad" and "narrow" types, composite states, built as combinations of broad and narrow beams with identical or opposite signs ("unipolar" and "bipolar" states, respectively), and "single-sided" broad and narrow beams trapped, essentially, in a single channel. The stability of the families is investigated via eigenvalues of…
We propose a new mechanism for stabilization of confined modes in lasers and semiconductor microcavities holding exciton-polariton condensates, with spatially uniform linear gain, cubic loss, and cubic self-focusing or defocusing nonlinearity. We demonstrated that the commonly known background instability driven by the linear gain can be suppressed by a combination of a harmonic-oscillator trapping potential and effective diffusion. Systematic numerical analysis of one- and two-dimensional (1D and 2D) versions of the model reveals a variety of stable modes, including stationary ones, breathers…
Dispersive shock waves in thermal optical media belong to the third-order nonlinear phenomena, whose intrinsic irreversibility is described by time asymmetric quantum mechanics. Recent studies demonstrated that nonlocal wave breaking evolves in an exponentially decaying dynamics ruled by the reversed harmonic oscillator, namely, the simplest irreversible quantum system in the rigged Hilbert spaces. The generalization of this theory to more complex scenarios is still an open question. In this work, we use a thermal third-order medium with an unprecedented giant Kerr coefficient, the M-Cresol/Ny…
We predict random-phase spatial solitons in instantaneous nonlocal nonlinear media. The key mechanism responsible for self-trapping of such incoherent wave-packets is played by the non-local (rather than the traditional non-instantaneous) nature of the nonlinearity. This new kind of incoherent solitons has profoundly different features than other incoherent solitons.
We demonstrate the existence of confined states in one- and two-dimensional (1D and 2D) systems of two linearly-coupled components, with the confining harmonic-oscillator (HO) potential acting upon one component, and an expulsive anti-HO potential acting upon the other. The systems ca be implemented in optical and BEC dual-core waveguides. In the 1D linear system, codimension-one solutions are found in an exact form for the ground state (GS) and dipole mode (the first excited state). Generic solutions are produced by means of the variational approximation, and are found in a numerical form. Ex…
We study localized modes (LMs) of the one-dimensional Gross-Pitaevskii/nonlinear Schrödinger equation with a harmonic-oscillator (parabolic) confining potential, and a periodically modulated coefficient in front of the cubic term (nonlinear lattice pseudopotential). The equation applies to a cigar-shaped Bose-Einstein condensate loaded in the combination of a magnetic trap and an optical lattice which induces the periodic pseudopotential via the Feshbach resonance. Families of stable LMs in the model feature specific properties which result from the interplay between spatial scales introduced …
We review the state of the art and recently obtained theoretical and experimental results for two- and three-dimensional (2D and 3D) solitons and related states, such as quantum droplets, in optical systems, atomic Bose-Einstein condensates (BECs), and other fields - in particular, liquid crystals. The central challenge is avoiding the trend of 2D and 3D solitary states supported by the ubiquitous cubic nonlinearity to be strongly unstable - a property far less present in one-dimensional systems. Many possibilities for the stabilization of multi-dimensional states have been theoretically propo…
We predict the existence of stable fundamental and vortical bright solitons in dipolar Bose-Einstein condensates (BECs) with repulsive dipole-dipole interactions (DDI). The condensate is trapped in the 2D plane with the help of the repulsive contact interactions whose local strength grows $\sim r^{4}$ from the center to periphery, while dipoles are oriented perpendicular to the self-trapping plane. The confinement in the perpendicular direction is provided by the usual harmonic-oscillator potential. The objective is to extend the recently induced concept of the self-trapping of bright solitons…
We numerically investigate spherically symmetric collapses in the Gross-Pitaevskii equation with attractive nonlinearity in a harmonic potential. Even below threshold for direct collapse, the wave function bounces off from the origin and may eventually become singular after a number of oscilla- tions in the trapping potential. This is reminiscent of the evolution of Einstein gravity sourced by a scalar field in Anti-de Sitter space where collapse corresponds to black hole formation. We carefully examine the long time evolution of the wave function for continuous families of initial states in o…
We consider self-trapping of topological modes governed by the one- and two-dimensional (1D and 2D) nonlinear-Schrodinger/Gross-Pitaevskii equation with effective single- and double-well (DW) nonlinear potentials induced by spatial modulation of the local strength of the self-defocusing nonlinearity. This setting, which may be implemented in optics and Bose-Einstein condensates, aims to extend previous studies, which dealt with single-well nonlinear potentials. In the 1D setting, we find several types of symmetric, asymmetric and antisymmetric states, focusing on scenarios of the spontaneous s…
We consider a curved chain of nonlinear oscillators and show that the interplay of curvature and nonlinearity leads to a number of qualitative effects. In particular, the energy of nonlinear localized excitations centered on the bending decreases when curvature increases, i.e. bending manifests itself as a trap for excitations. Moreover, the potential of this trap is double-well, thus leading to a symmetry breaking phenomenon: a symmetric stationary state may become unstable and transform into an energetically favorable asymmetric stationary state. The essentials of symmetry breaking are exami…
We consider the three-dimensional (3D) mean-field model for the Bose-Einstein condensate (BEC), with a 1D nonlinear lattice (NL), which periodically changes the sign of the nonlinearity along the axial direction, and the harmonic-oscillator trapping potential applied in the transverse plane. The lattice can be created as an optical or magnetic one, by means of available experimental techniques. The objective is to identify stable 3D solitons supported by the setting. Two methods are developed for this purpose: The variational approximation, formulated in the framework of the 3D Gross-Pitaevski…
Vector rogue wave (RW) formation and their dynamics in Rabi coupled two- and three-species Bose-Einstein condensates with spatially varying dispersion and nonlinearity are studied. For this purpose, we obtain the RW solution of the two- and three-component inhomogeneous Gross-Pitaevskii (GP) systems with Rabi coupling by introducing suitable rotational and similarity transformations. Then, we investigate the effect of inhomogeneity (spatially varying dispersion, trapping potential and nonlinearity) on vector RWs for two different forms of potential strengths, namely periodic (optical lattice) …
Quantum reflection refers to a non-vanishing reflection probability in the absence of a classically turning point. Much attention has been paid to such reflections due to their fundamental, intriguing physics and potential practical applications. Here we propose a scheme to realize a quantum reflection of nonlocal nonlinear optical beams in a cold Rydberg atomic gas via electromagnetically induced transparency working in a dispersion regime. Based on the long-range interaction between Rydberg atoms, we found that the system supports low-power nonlocal optical solitons. Such nonlocal solitons c…
