arXiv subjects

Dmitry A. Zezyulin

Publications and source records attributed to Dmitry A. Zezyulin.

At least 19 recordsLinked to original sources

arXiv2026

Metastable soliton necklaces confined by the boundary of a flattop region

We present quasistationary ring-shaped soliton necklaces in a two-component envelope propagating in a medium with competing cubic-quintic nonlinearity. Metastable propagation of soliton necklaces results from a balance of repulsion between adjacent out-of-phase solitons in one component and confinement by the boundary of a flattop region in the other. Numerical simulations demonstrate metastable propagation over about a hundred diffraction lengths, even with random noise added to the input envelopes. The maximum number of solitons in metastable necklaces can be controlled either by changing the size of individual solitons or by adjusting the width of the flattop region hosting the necklace.

physics.optics↗

arXiv2026

Quantized transport of solitons in Bose-Einstein condensates driven by spin-orbit coupling

We demonstrate that linear and nonlinear Thouless pumping can be realized in two-component elongated Bose-Einstein condensates using helicoidal spin-orbit coupling that slides with respect to a static optical lattice, identical for both spinor components. Stable quantized transport is found for solitons in semi-infinite and finite gaps, within certain intervals of chemical potentials and numbers of atoms. In the semi-infinite gap, the transport is arrested for solitons with sufficiently large number of atoms. We elucidate the important role of Zeeman splitting in the control of quantized transport, which disappears when the longitudinal component of the Zeeman field is removed.

cond-mat.quant-gas↗

arXiv2025

Double-flat-top half-vortices and self-bound solitary wave billiards in cubic-quintic media with intermodal attraction

We consider a bimodal light field envelope propagating in a bulk medium characterized by competing cubic and quintic nonlinearities. The subfields are coupled by a cross-phase modulation term and experience effective attraction. We find dynamically stable stationary states which have two distinct flat-top regions with different intensities. These solutions represent half-vortices, where the first and second components are essentially different and, in particular, carry different topological charges: zero for one component and nonzero for the other. The typical propagation of an unstable half-vortex leads to the splitting of the central vortex core into several fragments which quasielastically interact with the boundary of the flat-top region. This behavior is interpreted as a self-bound solitary wave billiard, where the emerging fragments are the billiard balls and the flat-top region is the dynamically deforming table.

physics.optics↗

arXiv2025

Transverse instability of hybrid solitons in the strong light-matter coupling regime

We investigate the transverse instability of two-component solitons forming in a planar waveguide operating in the regime of strong light-matter coupling. The instability emerges as a result of the coupling between transverse diffraction of the photonic component and nonlinearity of the material excitations. Solutions of three different forms are addressed which include bright, gray-dark, and gray-gray solitons. In the limit of long-wavelength transverse perturbations, the instability is described with an asymptotic expansion whose predictions agree with the results of numerical simulations. The dynamic development of instability of initially perturbed bright solitons leads to the formation of high-intensity spots in the photonic component. For gray-dark and dark-dark solitons, the transverse instability leads to the spontaneous nucleation of vortex-antivortex pairs which emerge in both fields as transient patterns.

nlin.PS↗

arXiv2025

Localized Floquet modes in arrays of out-of-phase curved waveguides with a quasiperiodic modulation

We study light propagation in an array of periodically curved waveguides consisting of pairs of waveguides with out-of-phase oscillations of waveguide centers. We compute the corresponding Floquet propagation constants and find pseudocollapses where the Floquet bands shrink and, respectively, light diffraction is significantly inhibited. When, in addition, the refractive index of the waveguides in the array have quasiperiodic modulation in the transverse direction, we establish the existence of Floquet modes localized in the transverse direction and periodic in the longitudinal direction. With increase of the depth of quasiperiodic modulation of the refractive index in the array, the localized Floquet modes emerge near the pseudocollapse points of the periodic array. In array with sufficiently high frequencies of waveguide oscillations, the localized Floquet modes can exist even for weak quasiperiodic modulation which is situated below the localization transition in the array of straight waveguides.

physics.optics↗

arXiv2024

Formation of nonlinear modes in one-dimensional quasiperiodic lattices with a mobility edge

We investigate the formation of steady states in one-dimensional Bose-Einstein condensates of repulsively interacting ultracold atoms loaded into a quasiperiodic potential created by two incommensurate periodic lattices. We study the transformations between linear and nonlinear modes and describe the general patterns that govern the birth of nonlinear modes emerging in spectral gaps near band edges. We show that nonlinear modes in a symmetric potential undergo both symmetry-breaking pitchfork bifurcations and saddle-node bifurcations, mimicking the prototypical behaviors of symmetric and asymmetric double-well potentials. The properties of the nonlinear modes differ for bifurcations occurring below and above the mobility edge. In the generic case, when the quasiperiodic potential consists of two incommensurate lattices with a nonzero phase shift between them, the formation of localized modes in the spectral gaps occurs through a cascade of saddle-node bifurcations. Because of the analogy between the Gross-Pitaevskii equation and the nonlinear Schrödinger equation, our results can also be applied to optical modes guided by quasiperiodic photonic lattices.

nlin.PS↗

arXiv2024

Double-flattop quantum droplets in low-dimensional Bose-Bose mixtures

We predict the existence of double-flattop quantum droplets in atomic Bose-Bose mixtures. Solutions of this type have two flattop regions of nearly uniform atomic density corresponding to a compressed central core surrounded by a rarefied layer. The birth of these double-flattop quantum droplets is analytically described using a perturbation theory, which in the leading order reduces the problem to the cubic nonlinear Schrödinger equation. Its properties are then used to predict the shape of double-flattop solutions and draw the conclusions about their stability. The analytical results apply to one- and multidimensional quantum droplets, provided that the energy density satisfies certain conditions. Using the numerical continuation from the asymptotic limit, we obtain the families of one- and two-dimensional double flattop quantum droplets and confirm the stability of the nodeless states of this type.

cond-mat.quant-gas↗

arXiv2024

Multipole quantum droplets in quasi-one-dimensional asymmetric mixtures

We study quantum droplets emerging in a quasi-one-dimensional asymmetric mixture of two atomic species with different intra-component coupling constants. We find that such mixtures support a rich variety of multipole quantum droplets, where the macroscopic wavefunction of one component changes its sign and features distinctive multipole structure, while the wavefunction of another component does not have zeros. Such multipole droplets have no counterparts in the reduced single-component model frequently used to describe symmetric one-dimensional mixtures. We study transformations of multipole states upon variation of the chemical potential of each component and demonstrate that quantum droplets can split into separated fundamental states, transform into flat-top multipoles, or into multipole component coupled to flat-top state with several humps on it, akin to anti-dark solitons. Multipole quantum droplets described here are stable in large part of their existence domain. Our findings essentially broaden the family of quantum droplet states emerging in the beyond-meanfield regime and open the way for observation of such heterostructured states in Bose-Bose mixtures.

cond-mat.quant-gas↗

arXiv2024

Enhanced mobility of quantum droplets in periodic lattices

We predict that one- and two-dimensional self-bound quantum droplets, forming in Bose-Einstein condensates in the presence of Lee-Huang-Yang (LHY) quantum corrections to the mean-field energy, may demonstrate exceptional mobility in periodic optical lattices and that they may exhibit considerable displacements across the lattice, remaining dynamically stable, even under weak initial phase kicks imparted to them. Mobility properties of quantum droplets are determined by their internal structure and strongly depend on the number of particles in them. We find that due to the peculiar effect of the LHY quantum corrections, odd (i.e., on-site centered) and even (i.e., intersite-centered) one-dimensional quantum droplets feature alternating mobility and immobility bands closely corresponding to the regions, where translational perturbation mode is unstable and stable, respectively. This picture becomes even richer in two-dimensional case, where odd-odd, even-odd or even-even quantum droplets also feature alternating mobility and immobility domains, and where, surprisingly, the droplet may be mobile in one direction, but immobile in the orthogonal direction. We link changes in mobility properties with multiple intersections of energy $E(μ)$ and norm $N(μ)$ dependencies for droplets with different internal structure.

cond-mat.quant-gas↗

arXiv2024

Stability restoration by asymmetric nonlinear states in non-Hermitian double-well potentials

We introduce a class of one-dimensional complex optical potentials that feature a nonlinearity-induced stability restoration, i.e., the existence of stable nonlinear modes propagating in a waveguide whose linear eigenmodes are unstable. The optical potential is an even function of the transverse coordinate, i.e., the system is parity symmetric but not parity-time symmetric. The stability restoration occurs for asymmetric stationary nonlinear modes that do not respect the parity symmetry. Stable nonlinear states exist either for focusing and defocusing nonlinearities. On the qualitative level the stability restoration cab be analyzed using a simple bimodal system. Its solutions enable systematic construction of stable stationary modes and more complex patterns with intensity periodically oscillating along the propagation distance.

physics.optics↗

arXiv2024

Multistable localized states in highly photonic polariton rings with a quasiperiodic modulation

We present a theoretical study of an exciton-polariton annular microcavity with an additional quasiperiodic structure along the ring which is implemented in the form of a bicosine dependence. We demonstrate that for a sufficiently strong quasiperiodic modulation, the microcavity features a sharp mobility edge separating a cluster of localized states from the rest of the spectrum consisting of states extended over the whole ring. Localized modes can be excited using a resonant pump whose topological charge determines the phase distribution of excited patterns. Repulsive polariton interactions make the resonance peaks distinctively asymmetric and enable the formation of multistable states which feature the attractor-like dynamical behavior \rev{and hysteresis}. We also demonstrate that the localized states can be realized in a biannular cavity that consists of two rings, each having periodic modulation, such that the periods of two modulations are different.

cond-mat.mes-hall↗

arXiv2023

Continuous families of non-Hermitian surface solitons

We show that surface solitons form continuous families in one-dimensional complex optical potentials of a certain shape. This result is illustrated by non-Hermitian gap-surface solitons at the interface between a uniform conservative medium and a complex periodic potential. Surface soliton families are parameterized by a real propagation constant. The range of possible propagation constants is constrained by the relation between the continuous spectrum of the uniform medium and the band-gap structure of the periodic potential.

physics.optics↗

arXiv2023

Quasi-one-dimensional harmonically trapped quantum droplets

We theoretically consider effectively one-dimensional quantum droplets in a symmetric Bose-Bose mixture confined in a parabolic trap. We systematically investigate ground and excited families of localized trapped modes which bifurcate from eigenstates of the quantum harmonic oscillator as the number of particles departs from zero. Families of nonlinear modes have nonmonotonous behavior of chemical potential on the number of particles and feature bistability regions. Excited states are unstable close to the linear limit, but become stable when the number of particles is large enough. In the limit of large density, we derive a modified Thomas-Fermi distribution. Smoothly decreasing the trapping strength down to zero, one can dynamically transform the ground state solution to the solitonlike quantum droplet, while excited trapped states break in several moving quantum droplets.

cond-mat.quant-gas↗

arXiv2023

Adiabatic theory of one-dimensional curved polariton waveguides

We construct a general theory of adiabatic propagation of spinor exciton-polaritons in waveguides of arbitrary shape, accounting for the effects of TE-TM splitting in linear polarizations and Zeeman splitting in circular polarizations. The developed theory is applied for the description of waveguides of periodically curved shape. We show that in this geometry the periodic rotation of the effective in-plane magnetic field produced by TE-TM interaction results in a nontrivial band-gap structure, which can be additionally tuned by application of an external magnetic field. It is also demonstrated, that spin-dependent interactions between polaritons lead to the formation of stable gap solitons.

cond-mat.mes-hall↗

arXiv2022

Nonlinear Schrödinger equations with amplitude-dependent Wadati potentials

Complex Wadati-type potentials of the form $V(x)=-w^2(x) + iw_x(x)$, where $w(x)$ is a real-valued function, are known to possess a number of intriguing features, unusual for generic non-Hermitian potentials. In the present work, we introduce a class of nonlinear Schrödinger-type problems which generalize the Wadati potentials by assuming that the base function $w(x)$ depends not only on the transverse spatial coordinate but also on the amplitude of the field. Several examples of prospective physical relevance are discussed, including models with the nonlinear dispersion or with the derivative nonlinearity. The numerical study indicates that the generalized model inherits the remarkable features of standard Wadati potentials, such as the existence of continuous soliton families, the possibility of symmetry-breaking bifurcations when the model obeys the parity-time symmetry, the existence of constant-amplitude waves, and the eigenvalue quartets in the linear-instability spectra. Our results deepen the current understanding of the interplay between nonlinearity and non-Hermiticity and expand the class of systems which enjoy the exceptional combination of properties unusual for generic dissipative nonlinear models.

nlin.PS↗

arXiv2022

Quartic asymmetric exchange for two-dimensional ferromagnets with trigonal prismatic symmetry

We suggest a possible origin of noncollinear magnetic textures in ferromagnets (FMs) with the $D_{3h}$ point group symmetry. The suggested mechanism is different from the Dzyaloshinskii-Moriya interaction (DMI) and its straightforward generalizations. The considered symmetry class is important because a large fraction of all single-layer intrinsic FMs should belong to it. In particular, so does a monolayer Fe$_3$GeTe$_2$. At the same time, DMI vanishes identically in materials described by this point group, in the continuous limit. We use symmetry analysis to identify the only possible contribution to the free energy density in two dimensions that is of the fourth order with respect to the local magnetization direction and linear with respect to its spatial derivatives. This contribution predicts long-range conical magnetic spirals with both the average magnetization and the average chirality dependent on the spiral propagation direction. We relate the predicted spirals to a recent experiment on Fe$_3$GeTe$_2$. Finally, we demonstrate that, for easy-plane materials, the same mechanism may stabilize bimerons.

cond-mat.mes-hall↗

arXiv2022

Bose-Einstein condensates in quasi-periodic lattices: bosonic Josephson junction, self-trapping, and multi-mode dynamics

Bose-Einstein condensates loaded in one-dimensional bichromatic optical lattices with constituent sublattices having incommensurate periods is considered. Using the rational approximations for the incommensurate periods, we show that below the mobility edge the localized states are distributed nearly homogeneously in the space and explore the versatility of such potentials. We show that superposition of symmetric and anti-symmetric localized can be used to simulate various physical dynamical regimes, known to occur in double-well and multi-well traps. As examples, we obtain an alternative realization of a bosonic Josephson junction, whose coherent oscillations display beatings or switching in the weakly nonlinear regime, describe selftrapping and four-mode dynamics, mimicking coherent oscillations and self-trapping in four-well potentials. These phenomena can be observed for different pairs of modes, which are localized due to the interference rather than due to a confining trap. The results obtained using few-mode approximations are compared with the direct numerical simulations of the one-dimensional Gross-Pitaevskii equation. The localized states and the related dynamics are found to persist for long times even in the repulsive condensates. We also described bifurcations of the families of nonlinear modes, the symmetry breaking and stable minigap solitons.

cond-mat.quant-gas↗

arXiv2022

Localization of ultracold atoms in incommensurate spin-orbit-coupling and Zeeman lattices

We consider a particle governed by a one-dimensional Hamiltonian in which artificial periodic spin-orbit coupling and Zeeman lattice have incommensurate periods. Using best rational approximations to such quasiperiodic Hamiltonian, the problem is reduced to description of spinor states in a superlattice. In the absence of a constant Zeeman splitting, the system acquires an additional symmetry, which hinders the localization. However, if the lattices are deep enough, then localized states can appear even for Zeeman field with zero or small mean value. Spatial distribution of localized modes is nearly uniform and is directly related to the topological properties of the effective superlattice: center-of-mass coordinates of modes are determined by Zak phases computed from the superlattice band structure. The best rational approximations feature the `memory' effect: each rational approximation holds the information about the energies and spatial distribution of the modes obtained under preceding, less accurate approximations. Dispersion of low-energy initial wavepackets is characterized by the law $\propto t^β$ with $β$ varying between $1/2$ at the initial stage and $1$ at longer, but still finite-time, evolution. The dynamics of initial wavepackets, exciting mainly localized modes, manifests quantum revivals.

cond-mat.quant-gas↗