arXiv subjects

Boris A. Malomed

Publications and source records attributed to Boris A. Malomed.

At least 235 records · Page 13Linked to original sources

arXiv2019

Immiscible and miscible states in binary condensates in the ring geometry

We report detailed investigation of the existence and stability of mixed and demixed modes in binary atomic Bose-Einstein condensates with repulsive interactions in a ring-trap geometry. The stability of such states is examined through eigenvalue spectra for small perturbations, produced by the Bogoliubov-de Gennes equations, and directly verified by simulations based on the coupled Gross-Pitaevskii equations, varying inter- and intra-species scattering lengths so as to probe the entire range of miscibility-immiscibility transitions. In the limit of the one-dimensional (1D) ring, i.e., a very narrow one, stability of mixed states is studied analytically, including hidden-vorticity (HV) modes, i.e., those with opposite vorticities of the two components and zero total angular momentum. The consideration of demixed 1D states reveals, in addition to stable composite single-peak structures, double- and triple-peak ones, above a certain particle-number threshold. In the 2D annular geometry, stable demixed states exist both in radial and azimuthal configurations. We find that stable radially-demixed states can carry arbitrary vorticity and, counter-intuitively, the increase of the vorticity enhances stability of such states, while unstable ones evolve into randomly oscillating angular demixed modes. The consideration of HV states in the 2D geometry expands the stability range of radially-demixed states.

cond-mat.quant-gas↗

arXiv2019

Dynamical control of solitons in a parity-time-symmetric coupler by periodic management

We consider a dual-core nonlinear waveguide with the parity-time (PT) symmetry, realized in the form of equal gain and loss terms carried by the coupled cores. To expand a previously found stability region for solitons in this system, and explore possibilities for the development of dynamical control of the solitons, we introduce "management" in the form of periodic sinusoidal variation of the loss-gain (LG) coefficients, along with synchronous variation of the inter-core coupling (ICC) constant. This system, which can be realized in optics (in the temporal and spatial domains alike), features strong robustness when amplitudes of the variation of the LG and ICC coefficients keep a ratio equal to that of their constant counterparts, allowing one to find exact solutions for PT-symmetric solitons. A stability region for the solitons is identified in terms of the management amplitude and period, as well as the soliton's amplitude. In the long-period regime, the solitons evolve adiabatically, making it possible to predict their stability boundaries in an analytical form. The system keeping the Galilean invariance, collisions between moving solitons are considered too.

nlin.PS↗

arXiv2019

Splitting of nonlinear-Schrödinger breathers by linear and nonlinear localized potentials

We consider evolution of one-dimensional nonlinear-Schrödinger (NLS) two-soliton complexes (breathers) with narrow repulsive or attractive potentials (barrier or well, respectively). By means of systematic simulations, we demonstrate that the breather may either split into constituent fundamental solitons (fragments) moving in opposite directions, or bounce as a whole from the barrier. A critical initial position of the breather, which separates these scenarios, is predicted by an analytical approximation. The narrow potential well tends to trap the fragment with the larger amplitude, while the other one escapes. The interaction of the breather with a nonlinear potential barrier is also considered. The ratio of amplitudes of the emerging free solitons may be different from the 3:1 value suggested by the exact NLS solution, especially in the case of the nonlinear potential barrier. Post-splitting velocities of escaping solitons may be predicted by an approximation based on the energy balance.

cond-mat.quant-gas↗

arXiv2019

Vortex solitons: Old results and new perspectives

A review is given of some well-known and some recent results for two- and three-dimensional (2D and 3D) solitons, with emphasis on states carrying embedded vorticity. Unlike typically stable 1D solitons, 2D and 3D ones are vulnerable to instabilities induced by the critical and supercritical collapse, respectively, in the 2D and 3D models with cubic focusing nonlinearity. Vortex solitons are subject to a still stronger splitting instability. For this reason, a central problem is looking for physical settings in which 2D and 3D solitons may be stabilized. The review addresses, first, two well-established topics, viz., the stabilization of vortex solitons by means of competing nonlinearities, or by trapping potentials (harmonic-oscillator and spatially-periodic ones). The former topic includes a new addition, viz., the prediction of robust quantum droplets. Two other topics outline new schemes elaborated for the creation of stable vortical solitons. One scheme relies on the use of spin-orbit coupling (SOC) in binary BEC, making it possible to predict stable 2D and 3D solitons, which couple or mix components with vorticities S=0 and (+/-)1 (semi-vortices (SVs) or mixed modes (MMs), respectively). In this system, the situation is different in the 2D and 3D geometries. In 2D, SOC helps to create a ground state (GS), represented by stable SV or MM solitons, whose norm falls below the threshold value at which the critical collapse sets in. In the 3D geometry, the supercritical collapse does not allow one to create a GS, but metastable solitons of the SV and MM types can be constructed. Another new scheme makes it possible to create stable 2D vortex-ring solitons with arbitrarily high S in a binary BEC with components coupled by microwave radiation. Some other topics are addressed too, such as vortex solitons in dissipative media and attempts to create vortex solitons in experiments.

physics.optics↗

arXiv2019

Attraction centers and PT-symmetric delta-functional dipoles in critical and supercritical self-focusing media

We introduce a model based on the one-dimensional nonlinear Schroedinger equation (NLSE) with the critical (quintic) or supercritical self-focusing nonlinearity. We demonstrate that a family of solitons, which are unstable in this setting against collapse, is stabilized by pinning to an attractive defect, that may also include a parity-time (PT)-symmetric gain-loss component. The model can be realized as a planar waveguide in optics, and in a super-Tonks-Girardeau bosonic gas. For the attractive defect with the delta-functional profile, a full family of the pinned solitons is found in an exact form. In the absence of the gain-loss term, the solitons' stability is investigated analytically too, by means of the Vakhitov-Kolokolov criterion; in the presence of the PT-balanced gain and loss, the stability is explored by means of numerical methods. In particular, the entire family of pinned solitons is stable in the quintic medium if the gain-loss term is absent. A stability region for the pinned solitons persists in the model with an arbitrarily high power of the self-focusing nonlinearity. A weak gain-loss component gives rise to alternations of stability and instability in the system's parameter plane. Those solitons which are unstable under the action of the supercritical self-attraction are destroyed by the collapse. If the self-attraction-driven instability is weak and the gain-loss term is present, unstable solitons spontaneously transform into localized breathers. The same outcome may be caused by a combination of the critical nonlinearity with the gain and loss. Instability of the solitons is also possible when the PT-symmetric gain-loss term is added to the subcritical nonlinearity. The system with self-repulsive nonlinearity is briefly considered too, producing completely stable families of pinned localized states.

nlin.PS↗

arXiv2019

Metastability of quantum droplet clusters

We show that metastable ring-shaped clusters can be constructed from two-dimensional quantum droplets in systems described by the Gross-Pitaevskii equations augmented with Lee-Huang-Yang quantum corrections. The clusters exhibit dynamical behaviours ranging from contraction to rotation with simultaneous periodic pulsations, or expansion, depending on the initial radius of the necklace pattern and phase shift between adjacent quantum droplets. We show that, using an energy-minimization analysis, one can predict equilibrium values of the cluster radius that correspond to rotation without radial pulsations. In such a regime, the clusters evolve as metastable states, withstanding abrupt variations in the underlying scattering lengths and keeping their azimuthal symmetry in the course of evolution, even in the presence of considerable perturbations.

cond-mat.quant-gas↗

arXiv2019

Symmetry breaking of quantum droplets in a dual-core trap

We consider the dynamical model of a binary bosonic gas trapped in a symmetric dual-core cigar-shaped potential. The setting is modeled by a system of linearly-coupled one-dimensional Gross-Pitaevskii equations with the cubic self-repulsive terms and quadratic attractive ones,which represent the Lee-Huang-Yang corrections to the mean-field theory in this geometry. The main subject is spontaneous symmetry breaking (SSB) of quantum droplets (QDs), followed by restoration of the symmetry, with respect to the symmetric parallel-coupled trapping cores, following the increase of the QD's total norm. The SSB transition and inverse symmetry-restoring one form a bifurcation loop, whose shape in concave at small values of the inter-core coupling constant, $κ$, and convex at larger $κ$. The loop does not exist above a critical value of $κ$. At very large values of the norm, QDs do not break their symmetry, featuring a flat-top shape. Some results are obtained in an analytical form, including an exact front solution connecting constant zero and finite values of the wave function. Collisions between moving QDs are considered too, demonstrating a trend to merger into breathers.

nlin.PS↗

arXiv2019

Two-dimensional composite solitons in Bose-Einstein condensates with spatially confined spin-orbit coupling

It was recently found that the spin-orbit (SO) coupling can help to create stable matter-wave solitons in spinor Bose-Einstein condensates in the two-dimensional (2D) free space. Being induced by external laser illumination, the effective SO coupling can be applied too in a spatially confined area. Using numerical methods and the variational approximation (VA), we build families of 2D solitons of the semi-vortex (SV) and mixed-mode (MM) types, and explore their stability, assuming that the SO-coupling strength is confined in the radial direction as a Gaussian. The most essential result is identification, by means of the VA and numerical methods, of the minimum size of the spatial confinement for which the 2D system maintains stable solitons of the SV and MM types.

nlin.PS↗

arXiv2019

A purely Kerr nonlinear model admitting flat-top solitons

We elaborate one- and two-dimensional (1D and 2D) models of media with self-repulsive cubic nonlinearity, whose local strength is subject to spatial modulation that admits the existence of flat-top solitons of various types, including fundamental ones, 1D multipoles, and 2D vortices. Previously, solitons of this type were only produced by models with competing nonlinearities. The present setting may be implemented in optics and Bose-Einstein condensates. The 1D version gives rise to an exact analytical solution for stable flat-top solitons, and generic families may be predicted by means of the Thomas-Fermi approximation. Stability of the obtained flat-top solitons is analyzed by means of linear-stability analysis and direct simulations. Fundamental solitons and 1D multipoles with $k=1$ and $2$ nodes, as well as vortices with winding number $m=1$, are completely stable. For multipoles with $k\geq 3$ and vortices with $m\geq 2$, alternating stripes of stability and instability are identified in their parameter spaces.

physics.optics↗

arXiv2019

New Frontiers in Multidimensional Self-Trapping of Nonlinear Fields and Matter

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 proposed over the years. Most strategies involve non-cubic nonlinearities or using different sorts of potentials, including periodic ones. New important avenues have arisen recently in systems based on two-component BEC with spin-orbit coupling, which have been predicted to support stable 2D and metastable 3D solitons. An important recent breakthrough is the creation of 3D quantum droplets. These are self-sustained states existing in two-component BECs, which are stabilized by the presence of Lee-Hung-Yang quantum fluctuations around the underlying mean-field states. By and large, multi-dimensional geometries afford unique opportunities to explore the existence of complex self-sustained states, including topologically rich ones, which by their very nature are not possible in one-dimensional geometries. In addition to vortex solitons, these are hopfions, skyrmions, and hybrid vortex-antivortex complexes, which have been predicted in different models. Here we review recent landmark findings in this field and outline outstanding open challenges.

physics.optics↗

arXiv2019

Robust PT symmetry of two-dimensional fundamental and vortex solitons supported by spatially modulated nonlinearity

The real spectrum of bound states produced by PT-symmetric Hamiltonians usually suffers breakup at a critical value of the strength of gain-loss terms, i.e., imaginary part of the complex potential. On the other hand, it is known that the PT-symmetry can be made unbreakable in a one-dimensional (1D) model with self-defocusing nonlinearity whose strength grows fast enough from the center to periphery. The model is nonlinearizable, i.e., it does not have a linear spectrum, while the (unbreakable) PT symmetry in it is defined by spectra of continuous families of nonlinear self-trapped states (solitons). Here we report results for a 2D nonlinearizable model whose PT symmetry remains unbroken for arbitrarily large values of the gain-loss coeffcient. Further, we introduce an extended 2D model with the imaginary part of potential ~ xy in the Cartesian coordinates. The latter model is not a PT-symmetric one, but it also supports continuous families of self-trapped states, thus suggesting an extension of the concept of the PT symmetry. For both models, universal analytical forms are found for nonlinearizable tails of the 2D modes, and full exact solutions are produced for particular solitons, including ones with the unbreakable PT symmetry, while generic soliton families are found in a numerical form. The PT-symmetric system gives rise to generic families of stable single- and double-peak 2D solitons (including higher-order radial states of the single-peak solitons), as well as families of stable vortex solitons with winding numbers m = 1, 2, and 3. In the model with imaginary potential ~ xy, families of single-and multi-peak solitons and vortices are stable if the imaginary potential is subject to spatial confinement. In an elliptically deformed version of the latter model, an exact solution is found for vortex solitons with m = 1.

physics.optics↗

arXiv2019

The variational reduction for low-dimensional Fermi gases and Bose - Fermi mixtures: A brief review

We present a summary of some recent theoretical results for matter-wave patterns in Fermi and Bose-Fermi degenerate gases, obtained in the framework of the quasi-mean-field approximation. We perform a dimensional reduction from the three-dimensional (3D) equations of motion to 2D and 1D effective equations. In both cases, comparison of the low-dimensional reductions to the full model is performed, showing very good agreement for ground-state solutions. Some complex dynamical regimes are reported too for the corresponding 1D systems.

cond-mat.quant-gas↗

arXiv2019

Interactions of solitons with positive and negative masses: Shuttle motion and co-acceleration

We consider a possibility to realize self-accelerating motion of interacting states with effective positive and negative masses in the form of pairs of solitons in two-component BEC loaded in an optical-lattice (OL) potential. A crucial role is played by the fact that gap solitons may feature a negative dynamical mass, keeping their mobility in the OL. First, the respective system of coupled Gross-Pitaevskii equations (GPEs) is reduced to a system of equations for envelopes of the lattice wave functions. Two generic dynamical regimes are revealed by simulations of the reduced system, viz., shuttle oscillations of pairs of solitons with positive and negative masses, and splitting of the pair. The co-accelerating motion of the interacting solitons, which keeps constant separation between them, occurs at the boundary between the shuttle motion and splitting. The position of the co-acceleration regime in the system's parameter space can be adjusted with the help of an additional gravity potential, which induces its own acceleration, that may offset the relative acceleration of the two solitons, while gravity masses of both solitons remain positive. The numerical findings are accurately reproduced by a variational approximation. Collisions between shuttling or co-accelerating soliton pairs do not alter the character of the dynamical regime. Finally, regimes of the shuttle motion, co-acceleration, and splitting are corroborated by simulations of the original GPE system, with the explicitly present OL potential.

nlin.PS↗

arXiv2019

Tail-free self-accelerating solitons and vortices

Self-accelerating waves in conservative systems, which usually feature slowly decaying tails, such as Airy waves, have drawn great interest in studies of quantum and classical wave dynamics. They typically appear in linear media, while nonlinearities tend to deform and eventually destroy them. We demonstrate, by means of analytical and numerical methods, the existence of robust one- and two-dimensional (1D and 2D) self-accelerating tailless solitons and solitary vortices in a model of two-component Bose-Einstein condensates, dressed by a microwave (MW) field, whose magnetic component mediates long-range interaction between the matter-wave constituents, with the feedback of the matter waves on the MW field taken into account. In particular, self-accelerating 2D solitons may move along a curved trajectory in the coordinate plane. The system may also include the spin-orbit coupling between the components, leading to similar results for the self-acceleration. The effect persists if the contact cubic nonlinearity is included. A similar mechanism may generate 1D and 2D self-accelerating solitons in optical media with thermal nonlinearity.

cond-mat.quant-gas↗

arXiv2018

Two-dimensional vortex quantum droplets

It was recently found that the Lee-Huang-Yang (LHY) correction to the mean-field Hamiltonian suppresses the collapse and creates stable localized modes (two-component "quantum droplets", QDs) in two and three dimensions. We construct two-dimensional\ self-trapped modes in the form of QDs with vorticity $S$ embedded into each component. The QDs feature a flat-top shape, which expands with the increase of $S$ and norm $N$. An essential finding, produced by a systematic numerical analysis and analytical estimates, is that the vortical QDs are \emph{stable} (which is a critical issue for vortex solitons in nonlinear models) up to $S=5$, for $N$ exceeding a certain threshold value. In the condensate of $^{39}$K atoms, in which QDs with $S=0$ and a quasi-2D shape were created recently, the vortical droplets may have radial size $\lesssim 30$ $\mathrmμ$m, with the number of atoms in the range of $10^{4}-10^{5}$. It is worthy to note that \textit{hidden-vorticity} states in QDs with topological charges $% S_{+}=-S_{-}=1$ in its components, which are prone to strong instability in other settings, have their stability region too, although it may be located beyond applicability limits of the underlying model. Dynamics of elliptically deformed QDs, which form rotating elongated patterns or ones with strong oscillations of the eccentricity, as well as collisions of QDs, are also addressed.

cond-mat.quant-gas↗

arXiv2018

Two-dimensional composite solitons in a spin-orbit-coupled Fermi gas in free space

We address a possibility of creating soliton states in oblate binary-fermionic clouds in the framework of the density-functional theory, which includes the spin-orbit coupling (SOC) and nonlinear attraction between spin-up and down-polarized components of the spinor wave function. In the limit when the inter-component attraction is much stronger than the effective intra-component Pauli repulsion, the resulting model also represents a system of Gross-Pitaevskii equations for a binary Bose-Einstein condensate including the SOC effect. We show that the model gives rise to two-dimensional quiescent composite solitons in free space. A stability region is identified for solitons of the mixed-mode type (which feature mixtures of zero-vorticity and vortical terms in both components), while solitons of the other type, semi-vortices (with the vorticity carried by one component) are unstable. Due to breaking of the Galilean invariance by SOC, the system supports moving solitons with velocities up to a specific critical value. Collisions between moving solitons are briefly considered too. The collisions lead, in particular, to a quasi-elastic rebound, or an inelastic outcome, which features partial merger of the solitons.

cond-mat.quant-gas↗

arXiv2018

Vortex modes supported by spin-orbit coupling in a laser with saturable absorption

We introduce a system of two component two-dimensional (2D) complex Ginzburg-Landau equations (CGLEs) with spin-orbit-coupling (SOC) describing a wide-aperture microcavity laser with saturable gain and absorption. We report families of two-component self-trapped dissipative laser solitons in this system. The SOC terms are represented by the second-order differential operators, which sets the difference, $|ΔS|=2$, between the vorticities of the two components. We have found stable solitons of two types: vortex-antivortex (VAV) and semi-vortex (SV) bound states, featuring vorticities $\left( -1,+1\right) $ and $\left( 0,2\right) $, respectively. In previous works, 2D localized states of these types were found only in models including a trapping potential, while we are dealing with the self-trapping effect in the latteraly unconfined (free-space) model. The SV states are stable in a narrow interval of values of the gain coefficients. The stability interval is broader for VAV states, and it may be expanded by making SOC stronger (although the system without SOC features a stability interval too). We have found three branches of stationary solutions of both VAV and SV types, two unstable and one stable. The latter one is an attractor, as the unstable states spontaneously transform into the stable one, while retaining vorticities of their components. Unlike previously known 2D localized states, maintained by the combination of the trapping potential and SOC, in the present system the VAV and SV complexes are stable in the absence of diffusion. In contrast with the bright solitons in conservative models, chemical potentials of the dissipative solitons reported here are positive.

nlin.PS↗

arXiv2018

Ring modes supported by concentrated cubic nonlinearity

We consider the one-dimensional Schroedinger equation on a ring, with the cubic term, of either self-attractive or repulsive sign, confined to a narrow segment. This setting can be realized in optics and Bose-Einstein condensates. For the nonlinearity coefficient represented by the delta-function, all stationary states are obtained in an exact analytical form. The states with positive chemical potentials are found in alternating bands for the cases of the self-repulsion and attraction, while solutions with negative chemical potentials exist only in the latter case. These results provide a possibility to obtain exact solutions for bandgap states in the nonlinear system. Approximating the delta-function by a narrow Gaussian, stability of the stationary modes is addressed through numerical computation of eigenvalues for small perturbations, and verified by simulations of the perturbed evolution. For positive chemical potentials, the stability is investigated in three lowest bands. In the case of the self-attraction, each band contains a stable subband, the transition to instability occurring with the increase of the total norm. As a result, multi-peak states may be stable in higher bands. In the case of the self-repulsion, a single-peak ground state is stable in the first band, while the two higher ones are populated by weakly unstable two- and four-peak excited states. In the case of the self-attraction and negative chemical potentials, single-peak modes feature instability which transforms them into persistently oscillating states.

physics.optics↗