arXiv subjects

Vladimir V. Konotop

Publications and source records attributed to Vladimir V. Konotop.

At least 19 recordsLinked to original sources

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

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↗

arXiv2026

Families of localized modes of Bose-Einstein condensates enabled by incommensurate optical lattice and photon-atom interactions

We consider a Bose-Einstein condensate (BEC) loaded into a one-dimensional optical cavity under the combined action of an external potential and atom-cavity coupling with mutually incommensurate periods. Such configuration enables the localization of matter waves even in the absence of two-body interactions. We study families of localized modes within the mean-field approximation for red and blue detunings from atomic and cavity resonances in relatively shallow quasiperiodic lattices, beyond the validity of the tight-binding approximation. The parameter regimes supporting localization of atomic wave packets are identified. The system exhibits two types of bistability manifested as distinct photon numbers under otherwise identical conditions. One type arises from the coexistence of multiple families of localized modes, typical of conservative nonlinear systems, while the other stems from the multivalued dependence of the families on system parameters, characteristic of systems exhibiting hysteresis. BEC in a cavity may also display pseudodegeneracy, understood as the existence of two distinct atomic-density distributions corresponding to the same atomic and photon numbers (although different chemical potentials). The stability of the localized modes is analyzed. It is shown that, owing to the strong impact of long-range interactions on stability, a two-localized-mode configuration can operate as an XOR logic gate.

cond-mat.quant-gas↗

arXiv2026

Half-vortex soliton lattices in spin-orbit-coupled Bose-Einstein condensates with a quasi-flat band

Periodic potentials with flat bands in their spectra support strongly localized nonlinear excitations. Although a perfectly flat band cannot exist in a continuous system, a spin-orbit-coupled Bose-Einstein condensate loaded in a Zeeman lattice can realize the quasi-flat lowest band with an extremely narrow bandwidth. In such a quasi flat band, half vortex solitons become confined within a single lattice cell, enabling the formation of arrays of coupled half vortex solitons arranged of various spatial geometries. In this work, we study the existence and stability of these lattices within the framework of the two-component Gross-Pitaevskii equation. We demonstrate that, near the quasi-flat band, half-vortex solitons and their arrays can be excited with a nearly negligible number of atoms and are constrained by their local symmetries, which are isomorphic to a dihedral group of order 8. This allows observation of the respective field patterns in the nearly linear regime where they exhibit enhanced stability. The constructed lattices may have diverse geometric profiles, and in particular create a composite super-half-vortex soliton with nonlinear symmetry breaking.

cond-mat.quant-gas↗

arXiv2025

Plasmon polariton assisted second-harmonic generation in graphene

In this paper we present a theoretical examination of second-harmonic generation (SHG) in a graphene monolayer integrated within an attenuated total internal reflection (ATR) configuration. By embedding graphene in this optical setup, we explore the enhancement in the nonlinear optical response, particularly focusing on the efficiency of SHG. Our analysis reveals that the excitation of surface plasmon-polaritons (SPPs) plays a central role in significantly boosting the efficiency of SHG. The unique electronic properties of graphene, combined with the resonant characteristics of SPPs, create a synergistic effect that amplifies the nonlinear optical signals. This enhancement is attributed to the strong field confinement and the resonant nature of SPPs, which effectively increase the interaction between the incident light and the graphene monolayer. Furthermore, we analyze the underlying mechanisms that govern this process, providing a comprehensive theoretical framework that elucidates the interplay between graphene's electronic structure and the optical fields. Our findings suggest that the ATR scheme not only facilitates the excitation of SPPs but also optimizes the conditions for SHG.

cond-mat.mes-hall↗

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

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

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↗

arXiv2025

Topological pumping of multi-frequency solitons

We report on the topological pumping of quadratic optical solitons, observed through their quantized transport in a dynamic optical potential. A distinctive feature of this system is that the two fields with different frequencies, which together form the quadratic soliton, evolve in separate yet topologically equivalent dynamic optical potentials. Pumping in this system exhibits several notable differences from pumping in cubic media. While Chern indices characterizing quantized transport for uncoupled fundamental and second harmonic waves are nonzero, small-amplitude solitons with narrow spectra do not move, thus revealing a non-topological phase. As the nonlinearity increases, the system undergoes a sharp transition, depending on the velocity of one of the sublattices forming dynamical potential, into the phase where the quantized transport of quadratic solitons governed by nonzero Chern numbers is observed. The power level at which this transition occurs increases with increase of pumping velocity, and the transition is observed even in the regime when the adiabatic approximation no longer applies. Unlike in cubic media, in a quadratic medium neither breakup of topological pumping nor fractional pumping at high power levels are observed.

physics.optics↗

arXiv2024

Observation of Thouless pumping of light in quasiperiodic photonic crystals

Topological transport is determined by global properties of physical media where it occurs and is characterized by quantized amounts of adiabatically transported quantities. Discovered for periodic potentials it was also explored in disordered and discrete quasi-periodic systems. Here we report on experimental observation of pumping of a light beam in a genuinely continuous incommensurate photorefractive quasi-crystal emulated by its periodic approximants. We observe a universal character of the transport which is determined by the ratio between periods of the constitutive sublattices, by the sliding angle between them, and by Chern numbers of the excited bands (in the time-coordinate space) of the approximant, for which pumping is adiabatic. This reveals that the properties of quasi-periodic systems determining the topological transport are tightly related to those of their periodic approximants and can be observed and studied in a large variety of physical systems. Our results suggest that the links between quasi periodic systems and their periodic approximants go beyond the pure mathematical relations: they manifest themselves in physical phenomena which can be explored experimentally.

physics.optics↗

arXiv2024

Observation of localization of light in photonic quasicrystals of diverse symmetries

Quasicrystals are ubiquitous in nature. Beyond crystalline solids, they can be created as optically induced or technologically fabricated structures in photonic and phononic systems, as potentials for cold atoms and Bose-Einstein condensates (BECs). On a parwith the unusual structural properties of quasicrystals, nowadays the problem of wave propagation in such two-dimensional structures attracts considerable attention, already in earlier studies it was predicted that the lowest electronic states in five-fold quasicrystals are localized. Later on localization of BECs in an eight-fold rotational symmetric quasicrystal optical lattices was observed. Direct observation of localization in purely linear photonic quasicrystals, therefore, remains elusive. Here, using sets of interfering plane waves, we create photonic two-dimensional quasicrystals with different rotational symmetries, not allowed in periodic crystallographic structures. We demonstrate experimentally that linear localization of light does occur even in clean linear quasicrystals for probe beams propagating both in the center and off-center regions of the quasicrystals. We found that light localization occurs above a critical depth of optically induced potential and that this critical depth rapidly decreases with the increase of the order of the discrete rotational symmetry of the quasicrystal. Our results clarify a long-standing problem of wave localization in linear quasicrystals and elucidate the conditions under which this phenomenon occurs. These findings pave the way for achieving wave localization in a wide variety of aperiodic systems obeying discrete symmetries, with possible applications in photonics, atomic physics, acoustics, and condensed matter.

physics.optics↗

arXiv2024

Dimers and discrete breathers in Bose-Einstein condensates in a quasi-periodic potential

A quasi-one-dimensional Bose-Einstein condensate loaded into a quasi-periodic potential created by two sub-lattices of comparable amplitudes and incommensurate periods is considered. Although the conventional tight-binding approximation is not applicable in this setting, the description can still be reduced to a discrete model that accounts for the modes below the mobility edge. In the respective discrete lattice, where no linear hopping exists, solutions and their dynamics are governed solely by nonlinear interactions. Families of nonlinear modes, including those with no linear limit, are described with a special focus on dimers, which correspond to breather solutions of the Gross-Pitaevskii equation with a quasi-periodic potential. The breathers are found to be stable for negative scattering lengths. Localization and stable propagation of breathers are also observed for positive scattering lengths at relatively weak and moderate nonlinearities.

quant-ph↗

arXiv2024

Two-dimensional flat-band solitons in superhoneycomb lattices

Flat-band periodic materials are characterized by a linear spectrum containing at least one band where the propagation constant remains nearly constant irrespective of the Bloch momentum across the Brillouin zone. These materials provide a unique platform for investigating phenomena related to light localization. Meantime, the interaction between flat-band physics and nonlinearity in continuous systems remains largely unexplored, particularly in continuous systems where the band flatness deviates slightly from zero, in contrast to simplified discrete systems with exactly flat bands. Here, we use a continuous superhoneycomb lattice featuring a flat band in its spectrum to theoretically and numerically introduce a range of stable flatband solitons. These solutions encompass fundamental, dipole, multi-peak, and even vortex solitons. Numerical analysis demonstrates that these solitons are stable in a broad range of powers. They do not bifurcate from the flat band and can be analyzed using Wannier function expansion leading to their designation as Wannier solitons. These solitons showcase novel possibilities for light localization and transmission within nonlinear flat-band systems.

nlin.PS↗

arXiv2024

Bloch-Landau-Zener oscillations in a quasi-periodic potential

Bloch oscillations and Landau-Zener tunneling are ubiquitous phenomena which are sustained by a band-gap spectrum of a periodic Hamiltonian and can be observed in dynamics of a quantum particle or a wavepacket in a periodic potential under action of a linear force. Such physical setting remains meaningful for aperiodic potentials too, although band-gap structure does not exist anymore. Here we consider the dynamics of noninteracting atoms and Bose-Einstein condensates in a quasi-periodic one-dimensional optical lattice subjected to a weak linear force. Excited states with energies below the mobility edge, and thus localized in space, are considered. We show that the observed oscillatory behavior is enabled by tunneling between the initial state and a state (or several states) located nearby in the coordinate-energy space. The states involved in such Bloch-Landau-Zener oscillations are determined by the selection rule consisting of the condition of their spatial proximity and condition of quasi-resonances occurring at avoided crossings of the energy levels. The latter condition is formulated mathematically using the Gershgorin circle theorem. The effect of the inter-atomic interactions on the dynamics can also be predicted on the bases of the developed theory. The reported results can be observed in any physical system allowing for observation of the Bloch oscillations, upon introducing incommensurablity in the governing Hamiltonian.

cond-mat.quant-gas↗

arXiv2023

Bound states in Bose-Einstein condensates with radially-periodic spin-orbit coupling

We consider Bose-Einstein condensate (BEC) subject to the action of spin-orbit-coupling (SOC) periodically modulated in the radial direction. In contrast to the commonly known principle that periodic potentials do not create bound states, the binary BEC maintains multiple localized modes in the linear limit, with their chemical potential falling into spectral gaps of the (numerically found) radial band structure induced by the spatial modulation of the SOC. In the presence of the repulsive nonlinearity, the SOC modulation supports fundamental gap solitons of the semi-vortex types, as well as higher-order vortex gap solitons. The localization degree and stability of the gap solitons strongly depend on the location of their chemical potential in the gap. Stability intervals for vortex gap solitons in a broad range of the intrinsic vorticity, from -2 to 3, are identified. Thus, the analysis reveals the previously unexplored mechanism of linear and nonlinear localization provided by the spatially periodic modulation of SOC, which may be extended to other settings, such as those for optical beams and polaritons. Unlike the commonly known quartets of eigenvalues for small perturbations, in the present system the instability is accounted for by shifted complex eigenvalue pairs.

cond-mat.quant-gas↗

arXiv2023

Vortex solitons in moire optical lattices

We show that optical moire lattices enable the existence of vortex solitons of different types in self-focusing Kerr media. We address the properties of such states both in lattices having commensurate and incommensurate geometries (i.e., constructed with Pythagorean and non-Pythagorean twist angles, respectively), in the different regimes that occur below and above the localization-delocalization transition. We find that the threshold power required for the formation of vortex solitons strongly depends on the twist angle and, also, that the families of solitons exhibit intervals where their power is a nearly linear function of the propagation constant and they exhibit strong stability. Also, in the incommensurate phase above the localization-delocalization transition, we found stable embedded vortex solitons whose propagation constants belong to the linear spectral domain of the system.

physics.optics↗

arXiv2022

Two-dimensional Thouless pumping of light in photonic moiré lattices

Continuous and quantized transports are profoundly different. The latter is determined by the global rather than local properties of a system, it exhibits unique topological features, and its ubiquitous nature causes its occurrence in many areas of science. Here we report the first observation of fully-two-dimensional Thouless pumping of light by bulk modes in a purpose-designed tilted moiré lattices imprinted in a photorefractive crystal. Pumping in such unconfined system occurs due to the longitudinal adiabatic and periodic modulation of the refractive index. The topological nature of this phenomenon manifests itself in the magnitude and direction of shift of the beam center-of-mass averaged over one pumping cycle. \rev{Our experimental results are supported by systematic numerical simulations in the frames of the continuous Schrödinger equation governing propagation of probe light beam in optically-induced photorefractive moiré lattice.} Our system affords a powerful platform for the exploration of topological pumping in tunable commensurate and incommensurate geometries.

physics.optics↗

arXiv2022

Topological Floquet bound states in the continuum

A honeycomb array of helical waveguides with zigzag-zigzag edges and a refractive index gradient orthogonal to the edges may support Floquet bound states in continuum (BICs). The gradient of the refractive index leads to strong asymmetry of the Floquet-Bloch spectrum. The mechanism of creation of such Floquet BICs is understood as emergence of crossings and avoided crossings of the branches supported by spatially limited stripe array. The whole spectrum of a finite array is split into the bulk branches being continuation of the edge states in the extended zone revealing multiple self-crossings and bulk modes disconnected from the gap states by avoided crossing. Nearly all states in the system are localized due to the gradient, but topological edge states manifest much stronger localization than other states. Such strongly localized Floquet BICs coexist with localized Wannier-Stark-like bulk modes. Robustness of the edge Floquet states is confirmed by their passage through a localized edge defect in the form of a missing waveguide.

physics.optics↗