arXiv subjects

Yaroslav V. Kartashov

Publications and source records attributed to Yaroslav V. Kartashov.

At least 19 recordsLinked to original sources

arXiv2026

Stable three-dimensional lattice solitons in spin-orbit-coupled Bose-Einstein condensates

We address three-dimensional (3D) solitons maintained by spin-orbit coupling (SOC) in the binary self-interacting Bose-Einstein condensate (BEC) held in the 3D optical lattice (OL). The analysis reveals that the SOC-OL interplay results in the formation of stable full-vortex (FV) soli-tons, built as sets of four density peaks residing in neighboring wells of the lattice potential, with the superimposed global vortical phase, and site-centered semi-vortices (SV), in which the vorticity is present in only one component. The full-vortex solitons, with their specific phase textures, do not exist in a uniform BEC with SOC. Full-vortex and semi-vortex states in the binary self-attractive BEC are stable despite the possibility of the supercritical collapse in the 3D system. Such states also exist, as gap solitons, in the self-repulsive 3D system. In terms of the chemical potential and number of particles, the stability regions of the 3D full-vortex solitons and semi-vortices expand with the increase of the SOC strength and OL depth. The results open the route to the creation of 3D complexes of vorticity-carrying condensates that can be realized with existing experimental techniques.

cond-mat.quant-gas↗

arXiv2026

Vortex solitons in star networks

I consider vortex solitons in two-dimensional star networks created by several one-dimensional line waveguide arrays (or rays) brought in close proximity. First waveguide in each array belongs to the ring of certain radius and its modal field overlaps with modal fields of waveguides from other rays laying on this ring, as well as with modal fields of waveguides in this line array. This creates a system with discrete rotational symmetry that is capable of supporting various localized linear vortex states due to local coupling between waveguides on the central ring, where line arrays approach each other. Localized vortex states emerge from the continuum of the states extended along the rays of the structure upon variation of the radius of the central ring. I show how different vortex modes with progressively increasing topological charges emerge when the number of rays in structure and, therefore, its discrete rotational symmetry increases. Each such linear localized mode gives rise to a family of thresholdless vortex solitons in nonlinear optical medium, whose topological charges are limited by the discrete rotational symmetry of the system. Vortex solitons in star networks exhibit qualitatively different behavior with increasing power depending on whether the propagation constant of linear vortex that gives rise to a family of solitons is located above or below the band of extended states. Stability properties of vortex solitons nontrivially depend on their topological charge and discrete rotational symmetry of the system, showing very different picture from usual ring-like waveguide arrays.

physics.optics↗

arXiv2026

Thresholdless corner vortex solitons in fractal Sierpiński topological insulators

Quantized vortices are ubiquitous in physics, spanning superconductivity, astrophysics, superfluid condensed matter systems, and nonlinear optics. Yet embedding vorticity into topologically protected nonlinear states has remained a major challenge, with all previously observed corner solitons in higher-order topological insulators (HOTIs) exhibiting only trivial phase distributions. Here, we report on the first realization of stable topological corner vortex solitons in a photonic fractal HOTI. Using an array of laser-written waveguides in the shape of Sierpiński gasket with a controllable distortion, we design linear topological vortex modes, from which nonlinear corner vortex solitons bifurcate. Moreover, we demonstrate that these solitons exhibit exceptional robustness across a broad power range and, unlike vortex solitons in topologically trivial lattices, form without a power threshold. Our results introduce the angular momentum degree of freedom into the physics of topological corner modes, opening prospects for topologically protected vortex-based photonics.

physics.optics↗

arXiv2026

Quantized transport of two-dimensional multifrequency solitons

We consider Thouless pumping of two-dimensional quadratic solitons composed from coherently interacting fundamental frequency (FF) and second harmonic (SH) components propagating in a periodic $χ^{(2)}$ material. The pumping is induced by two mutually sliding two-dimensional lattices defined by shallow transverse and longitudinal periodic refractive index modulation. Focusing on solitons in the semi-infinite gap, we find three distinct pumping scenarios: the absence of transport for small-amplitude solitons, non-quantized transport in a transient regime at intermediate amplitudes, and stable quantized transport for solitons with relatively large amplitudes. Different directions of the sliding velocity were investigated resulting in different trajectories of soliton center. The transition to the regime of quantized transport is found to depend strongly on phase mismatch between FF and SH waves that also influences stability properties of two-dimensional $χ^{(2)}$ lattice solitons. We also show that pumping with longitudinal periods in the x and y directions, whose ratio approximates an irrational number, induces quantized transport whose direction rapidly converges, with increase of the accuracy of the approximation, to a limiting pumping direction determined by this irrational number and corresponding to truly incommensurate longitudinal periods.

physics.optics↗

arXiv2026

Stable rotating vortex clusters in three-dimensional quantum droplets

We predict a new type of stable three-dimensional (3D) vortex quantum droplets in binary Bose-Einstein condensate arranged into ring clusters that per-sistently rotate in the external potential. In contrast to clusters composed from localized quantum droplets, the states introduced here represent interacting vortex lines with identical topological charges nested in common 3D envelope and existing in much broader parameter range in comparison with local-ized quantum droplets. The intricate interplay between mean-field nonlinearity of Bose-Einstein condensate, quantum fluctuations described by Lee-Huang-Yang correction, Coriolis force arising due to rotation, and external potential leads to substantial variations of cluster shape upon increase of its rotation frequency. Rotating vortex clusters bifurcate from single-vortex quantum droplets and exist only above critical value of the rotation frequency that decreases with increase of chemical potential and depends on the number of vortex lines in the cluster. The radius of the cluster decreases with increase of rotation frequency and weakly varies with chemical potential, which determines mostly localization of the individual vortices in cluster and overall width of its envelope. Vortex droplet clusters are very robust objects existing in stable form in wide intervals of the number of particles for any number (odd or even) of vortex lines forming them. Our results may open the route to observation of stable arrays of vortex lines of different configurations per-forming regular collective motion in condensate.

nlin.PS↗

arXiv2026

Polariton Topological Insulators with Disclinations

We introduce polariton topological insulator on aperiodic array of microcavity pillars with disclination. This unique dissipative and nonlinear topological system can have discrete rotational symmetry not achievable in structures constructed on periodic arrays that qualitatively affects the structure of topological modes. In such system resonant optical pump can be used for selective excitation of topological states forming on the disclination core in the center, while imposing vorticity on the pump profile allows to excite not only the simplest disclination states, but also vortex-carrying disclination states. Strong repulsive nonlinearity of polaritonic system leads to increasing with pump amplitude tilt of the resonance curves and bistability, with rich possibilities for control of shapes of nonlinear disclination states within topological gap by pump frequency detuning. Stability analysis predicts remarkable robustness of both vortex-free and vortex-carrying nonlinear disclination states in this system. We show that when topological charge of the pump exceeds maximal allowed charge in the disclination array with a given discrete rotational symmetry, the stationary states form that contain vortex clusters in their phase distributions. Our results extend the concept of topo-logical insulators with disclinations to the realm of nonlinear resonantly driven systems and show that rich bistability effects in them can be observed even for excited vortex-carrying topological states with different topological charges allowed by discrete rotational symmetry of the system.

physics.optics↗

arXiv2026

Bistable topological edge states in polariton microcavities with unpaired Dirac cones

Among the most intriguing properties of honeycomb lattices is the presence of Dirac points that typically emerge in pairs, which can be destroyed by physical effects breaking certain symmetries of the system and leading to nontrivial band topology. We propose a nonlinear microcavity system supporting condensate of exciton-polaritons, where simultaneous breakup of inversion and time-reversal symmetries results in unusual spectrum with unpaired Dirac cones, profoundly affecting the properties of unidirectional edge states. Realized as an array of microcavity pillars, the inversion symmetry is broken by fission of pillar belonging to one of sublattices of honeycomb array into three pillars, while time-reversal symmetry is broken due to interplay of Zeeman splitting in the external magnetic field and spin-orbit coupling. Despite the absence of complete spectral gap, unidirectional edge states may still emerge that can circumvent array corners. Resonant optical pumping leads to reach bistability effects and allow selective excitation of the edge states. We obtain first example of stable localized dissipative edge soliton that circulates along the periphery of insulator over indefinitely long times without radiation. Our results suggest a new platform for nonlinear topological photonics and reveal nontrivial interplay between unpaired Dirac cones and nonlinear effects.

physics.optics↗

arXiv2026

Observation of an aperiodic polariton monotile

A plethora of unconventional localization phenomena and fractal features of linear spectrum observed in quasiperiodic structures have been accompanied by a long-standing quest for the geometrical elements and structures that permit tilings of the plane, but only in a non-periodic manner. Until 2024, it was believed that such quasiperiodic structures, or quasicrystals, could only be composed of at least two different tiles. Surprisingly, a newly discovered class of quasicrystals requires only one elementary monotile. However, its physical realization and study of propagating coherent excitations in this novel setting remained elusive. Here we optically sculpt aperiodic quasicrystals composed of "einstein" monotiles in an inorganic microcavity and observe nontrivial relative phases of the exciton-polariton condensates nonresonantly excited at the vertices of each monotile. Utilizing energy-resolved tomography in momentum-space, we reveal the formation of distinct Bragg peaks with six-fold symmetry and Dirac-like spectral fingerprints, intrinsic to the underlying graphene-like structure, while interferometric phase reconstruction shows a nontrivial synchronization pattern distinct from both periodic triangular lattices and Penrose quasicrystals. Our work demonstrates that monotiles can be converted into a programmable driven-dissipative artificial material, where long-range coherence coexists with enforced geometric aperiodicity, producing synchronization and spectral responses distinct from both periodic and conventional quasicrystalline tilings.

cond-mat.quant-gas↗

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

Observation of nonlinear higher-order topological insulators with unconventional boundary truncations

In higher-order topological insulators (HOTIs), topologically nontrivial phases are usually associated with the shift of Wannier centers to topologically nontrivial positions on the edges of the unit cells, and the emergence of fractional spectral charges in the corners of the lattice upon its truncation that keeps the number of its unit cells integer. Here we propose theoretically and illustrate experimentally a different approach to the construction of HOTIs. This approach utilizes lattices with incomplete unit cells and achieves localized modes of topological origin across a broader parameter space. When truncation disrupts translational symmetry by cutting through the interior of multiple unit cells, boundary modes in our system emerge for both trivial and topologically nontrivial positions of the Wannier centers. We link these modes to the appearance of fractional Wannier centers. We also demonstrate that linear boundary states give rise to rich families of stable solitons bifurcating from them in the presence of focusing nonlinearity. Multiple types of thresholdless topological solitons with different internal symmetries are observed in waveguide arrays with triangular configurations featuring incomplete unit cells for any dimerization of waveguide spacings. Our results expand the family of HOTIs and pave the way for the observation of boundary states with different symmetries.

physics.optics↗

arXiv2025

Fractal Polariton Topological Insulator

We introduce higher order polariton topological insulator (HOTI) realized with fractal array of microcavity pillars arranged into Sierpinski gasket-like geometry. This system exhibiting self similarity in different generations, can support localized modes either in the external or multiple internal corners depending on the controllable distortion introduced into first generation structure. Nonlinear corner modes can be selectively excited in this dissipative system using resonant optical pumping. Strong polariton-polariton interactions lead to tilt of the resonance curves and bistability as the pump amplitude increases, allowing control over corner state profiles. Linear stability analysis illustrates dynamical stability of such states. Our results show how nontrivial topology manifests itself in self similar, aperiodic structures and indicate that fractal geometry may bring qualitatively new localization scenarios in polariton HOTIs.

physics.optics↗

arXiv2025

Hopfions in the Lee-Huang-Yang superfluids

It is known that, under appropriate conditions, mean-field interactions can be canceled in binary BEC, leading to the formation of the Lee-Huang-Yang (LHY) superfluid, in which the nonlinearity is solely represented by the quartic LHY term. In this work we systematically investigate the existence, stability and evolution of hopfion states in this species of quantum matter. They are characterized by two independent topological winding numbers: inner twist $s$ of the vortex-ring core and overall vorticity $m$. The interplay between the LHY self-repulsion and a trapping harmonic-oscillator potential results in stability of the hopfions with $s = 1$ and $m$ ranging from $0$ to $4$. The hopfions exhibit distinct topological phase distributions along the vertical axis and the radial direction in the horizontal plane. Their effective radius and peak density increase with the chemical potential, along with expansion of the vortex-ring core. Although the instability domain of the hopfion modes broadens with the increase of $m$, stable hopfions persist in a wide range of the chemical potential, up to $m=4$, at least, provided that the norm exceeds a certain threshold value. The predictions are experimentally accessible in currently used BEC setups.

cond-mat.quant-gas↗

arXiv2025

Bloch-Landau-Zener Oscillations in Moiré Lattices

We develop a theory of two-dimensional Bloch-Landau-Zener (BLZ) oscillations of wavepackets in incommensurate moiré lattices under the influence of a weak linear gradient. Unlike periodic systems, aperiodic lattices lack translational symmetry and therefore do not exhibit a conventional band-gap structure. Instead, they feature a mobility edge, above which (in the optical context) all modes become localized. When a linear gradient is applied to a moiré lattice, it enables energy transfer between two or several localized modes, leading to the oscillatory behavior referred to as BLZ oscillations. This phenomenon represents simultaneous tunneling in real space and propagation constant (energy) space, and it arises when quasi-resonance condition for propagation constants and spatial proximity of interacting modes (together constituting a selection rule) are met. The selection rule is controlled by the linear gradient, whose amplitude and direction play a crucial role in determining the coupling pathways and the resulting dynamics. We derive a multimode model describing BLZ oscillations in the linear regime and analyze how both attractive and repulsive nonlinearities affect their dynamics. The proposed framework can be readily extended to other physical systems, including cold atoms and Bose-Einstein condensates in aperiodic potentials.

physics.optics↗

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↗

arXiv2025

Topological pumping of light governed by Fibonacci numbers

Topological pumping refers to transfer of a physical quantity governed by the systemtopology, resulting in quantized amounts of the transferred quantities. It is a ubiqui-tous wave phenomenon typically considered subject to exactly periodic adiabatic vari-ation of the system parameters. Recently, proposals for generalizing quasi-periodictopological pumping and identifying possible physical settings for its implementa-tion have emerged. In a strict sense, pumping with incommensurate frequencies canonly manifest over infinite evolution distances, raising a fundamental question aboutits observability in real-world finite-dimensional systems. Here we demonstrate thatbi-chromatic topological pumping with two frequencies, whose ratio is an irrationalnumber, can be viewed as the convergence limit of pumping with two commensuratefrequencies representing the best rational approximations of that irrational number. In our experiment, this phenomenon is observed as the displacement of a light beamcenter in photorefractive crystals induced by two optical lattices. The longitudinalperiods of the lattices, that in the paraxial approximation emulate two pumping fre-quencies, are related as Fibonacci numbers, successively approaching the golden ratio. We observed that a one-cycle displacement of the beam center at each successiveapproximation is determined by the relation between successive Fibonacci numbers,while the average direction of propagation (emulating average pumping velocity) ofthe beam is determined by the golden ratio.

physics.optics↗

arXiv2025

Observation of nonlinear topological corner states originating from different spectral charges

Higher-order topological insulators (HOTIs) are unique topological materials supporting edge states with the dimensionality at least by two lower than the dimensionality of the underlying structure. HOTIs were observed on lattices with different symmetries, but only in geometries, where truncation of HOTI produces a finite structure with the same order of discrete rotational symmetry as that of the unit cell, thereby setting the geometry of insulator edge. Here we experimentally demonstrate a new type of two-dimensional (2D) HOTI based on the Kekule-patterned lattice, whose order of discrete rotational symmetry differs from that of the unit cells of the constituent honeycomb lattice, with hybrid boundaries that help to produce all three possible corners that support effectively 0D corner states of topological origin, especially the one associated with spectral charge 5/6. We also show that linear corner states give rise to rich families of stable hybrid nonlinear corner states bifurcating from them in the presence of focusing nonlinearity of the material. Such new types of nonlinear corner states are observed in hybrid HOTI inscribed in transparent nonlinear dielectric using fs-laser writing technique. Our results complete the class of HOTIs and open the way to observation of topological states with new internal structure and symmetry.

physics.optics↗

arXiv2025

Self-Accelerating Topological Edge States

Edge states emerging at the boundaries of materials with nontrivial topology are attractive for many practical applications due to their remarkable robustness to disorder and local boundary deformations, which cannot result in scattering of the energy of the edge states impinging on such defects into the bulk of material, as long as forbidden topological gap remains open in its spectrum. The velocity of the such states traveling along the edge of the topological insulator is typically determined by their Bloch momentum. In contrast, here, using valley Hall edge states forming at the domain wall between two honeycomb lattices with broken inversion symmetry, we show that by imposing Airy envelope on them one can construct edge states which, on the one hand, exhibit \textit{self-acceleration} along the boundary of the insulator despite their fixed Bloch momentum and, on the other hand, \textit{do not diffract} along the boundary despite the presence of localized features in their shapes. We construct both linear and nonlinear self-accelerating edge states, and show that nonlinearity considerably affects their envelopes. Such self-accelerating edge states exhibit self-healing properties typical for nondiffracting beams. Self-accelerating valley Hall edge states can circumvent sharp corners, provided the oscillating tail of the self-accelerating topological state is properly apodized by using an exponential function. Our findings open new prospects for control of propagation dynamics of edge excitations in topological insulators and allow to study rich phenomena that may occur upon interactions of nonlinear envelope topological states.

physics.optics↗

arXiv2025

Thouless pumping of solitons in a nonlocal medium

Thouless pumping is a fundamental phenomenon recognized as being widespread across various areas of physics, with optics holding a particularly prominent role. Here, we study this effect for optical solitons in a medium where the refractive index is shaped by two slowly sliding sublattices and a nonlocal nonlinear response. The spectral bands of such a potential can exhibit nontrivial topology, and excitations occupying these bands can undergo quantized transport governed by the space -- time Chern indices of the linear spectrum. We find that nonlocality of the medium profoundly affects the dynamics of Thouless pumping. Thus, we show that broad, low-power fundamental solitons do not exhibit transport, as they excite only a small portion of the spectral band, while high-power solitons with broader spectral projections do demonstrate stable quantized transport. The transition point between these two principally different light propagation regimes strongly depends on the degree of nonlocality of the nonlinear response and shifts to larger powers with increasing nonlocality. Notably, even a moderate level of nonlocality is sufficient to prevent the breakdown of topological transport at high powers commonly observed in local Kerr media. Beyond fundamental solitons, we also demonstrate that multipole solitons, such as dipole and tripole states can be pumped stably. This is the first time such complex soliton states have been shown to undergo Thouless pumping. While fundamental solitons require only exceeding a power threshold, multipoles exhibit stable transport only within a finite power window. This window is broader for dipoles than for tripoles and expands with increasing nonlocality, revealing a trade-off between structural complexity and stability.

nlin.PS↗