arXiv subjects

Boris A. Malomed

Publications and source records attributed to Boris A. Malomed.

At least 487 records · Page 27Linked to original sources

arXiv2009

Application of the Feshbach-resonance management to a tightly confined Bose-Einstein condensate

We study suppression of the collapse and stabilization of matter-wave solitons by means of time-periodic modulation of the effective nonlinearity, using the nonpolynomial Schroedinger equation (NPSE) for BEC trapped in a tight cigar-shaped potential. By means of systematic simulations, a stability region is identified in the plane of the modulation amplitude and frequency. In the low-frequency regime, solitons feature chaotic evolution, although they remain robust objects.

cond-mat.quant-gas↗

arXiv2009

Magnetooptical control of light collapse in bulk Kerr media

Magneto-optical crystals allow an efficient control of the birefringence of light via the Cotton-Mouton and Faraday effects. These effects enable a unique combination of adjustable linear and circular birefringence, which, in turn, can affect the propagation of light in nonlinear Kerr media. We show numerically that the combined birefringences can accelerate, delay, or arrest the nonlinear collapse of (2+1)D beams, and report an experimental observation of the acceleration of the onset of collapse in a bulk Yttrium Iron Garnet (YIG) crystal in an external magnetic field.

nlin.PS↗

arXiv2009

Stable two-dimensional solitons in nonlinear lattices

We address the existence and stability of two-dimensional solitons in optical or matter-wave media, which are supported by purely nonlinear lattices in the form of a periodic array of cylinders with self-focusing nonlinearity, embedded into a linear material. We show that such lattices can stabilize two-dimensional solitons against collapse. We also found that stable multipoles and vortex solitons are also supported by the nonlinear lattices, provided that the nonlinearity exhibits saturation.

physics.optics↗

arXiv2008

Two-component gap solitons with linear interconversion

We consider one-dimensional solitons in a binary Bose-Einstein condensate with linear coupling between the components, trapped in an optical-lattice potential. The inter-species and intra-species interactions may be both repulsive or attractive. Main effects considered here are spontaneous breaking of the symmetry between components in symmetric and antisymmetric solitons, and spatial splitting between the components. These effects are studied by means of a variational approximation and numerical simulations.

cond-mat.other↗

arXiv2008

Stabilization of two-dimensional solitons and vortices against supercritical collapse by lattice potentials

It is known that optical-lattice (OL) potentials can stabilize solitons and solitary vortices against the critical collapse, generated by the cubic attractive nonlinearity in the 2D geometry. We demonstrate OLs can also stabilize various species of fundamental and vortical solitons against the super-critical collapse, driven by the double-attractive cubic-quintic nonlinearity (however, solitons remain unstable in the case of the pure quintic nonlinearity). Two types of OLs are considered, producing similar results: the 2D Kronig-Penney "checkerboard", and the sinusoidal potential. Soliton families are obtained by means of a variational approximation, and as numerical solutions. The stability of the families, which include fundamental and multi-humped solitons, vortices of oblique and straight types, vortices built of quadrupoles, and supervortices, strictly obeys the Vakhitov-Kolokolov criterion. The model applies to optical media and BEC in "pancake" traps.

nlin.PS↗

arXiv2008

Gap solitons on a ring

We introduce a new species of gap solitons (GSs) supported by an azimuthally modulated guiding ring in defocusing cubic media. The periodicity in the azimuthal direction strongly modifies properties and existence domains of GSs. In addition to the fundamental solitons, we report even and twisted bound states. The former type is found to be stable, while the twisted states are always unstable in defocusing media.

physics.optics↗

arXiv2008

Spontaneous symmetry breaking in a nonlinear double-well structure

We propose a model of a nonlinear double-well potential (NDWP), alias a double-well pseudopotential, with the objective to study an alternative implementation of the spontaneous symmetry breaking (SSB) in Bose-Einstein condensates (BECs) and optical media, under the action of a potential with two symmetric minima. In the limit case when the NDWP structure is induced by the local nonlinearity coefficient represented by a set of two delta-functions, a fully analytical solution is obtained for symmetric, antisymmetric and asymmetric states. In this solvable model, the SSB bifurcation has a fully subcritical character. Numerical analysis, based on both direct simulations and computation of stability eigenvalues, demonstrates that, while the symmetric states are stable up to the SSB bifurcation point, both symmetric and emerging asymmetric states, as well as all antisymmetric ones, are unstable in the model with the delta-functions. In the general model with a finite width of the nonlinear-potential wells, the asymmetric states quickly become stable, simultaneously with the switch of the SSB bifurcation from the subcritical to supercritical type. Antisymmetric solutions may also get stabilized in the NDWP structure of the general type, which gives rise to a bistability between them and asymmetric states. The symmetric states require a finite norm for their existence, an explanation to which is given. A full diagram for the existence and stability of the trapped states in the model is produced. Experimental observation of the predicted effects should be possible in BEC formed by several hundred atoms.

cond-mat.other↗

arXiv2008

Solitons in one-dimensional photonic crystals

We report results of a systematic analysis of spatial solitons in the model of 1D photonic crystals, built as a periodic lattice of waveguiding channels, of width D, separated by empty channels of width L-D. The system is characterized by its structural "duty cycle", DC = D/L. In the case of the self-defocusing (SDF) intrinsic nonlinearity in the channels, one can predict new effects caused by competition between the linear trapping potential and the effective nonlinear repulsive one. Several species of solitons are found in the first two finite bandgaps of the SDF model, as well as a family of fundamental solitons in the semi-infinite gap of the system with the self-focusing nonlinearity. At moderate values of DC (such as 0.50), both fundamental and higher-order solitons populating the second bandgap of the SDF model suffer destabilization with the increase of the total power. Passing the destabilization point, the solitons assume a flat-top shape, while the shape of unstable solitons gets inverted, with local maxima appearing in empty layers. In the model with narrow channels (around DC =0.25), fundamental and higher-order solitons exist only in the first finite bandgap, where they are stable, despite the fact that they also feature the inverted shape.

physics.optics↗

arXiv2008

Stability of temporal solitons in uniform and "managed" quadratic nonlinear media with opposite group-velocity dispersions at fundamental and second harmonics

The problem of the stability of solitons in second-harmonic-generating media with normal group-velocity dispersion (GVD) in the second-harmonic (SH) field, which is generic to available chi^(2) materials, is revisited. Using an iterative numerical scheme to construct stationary soliton solutions, and direct simulations to test their stability, we identify a full soliton-stability range in the space of the system's parameters, including the coefficient of the group-velocity-mismatch (GVM). The soliton stability is limited by an abrupt onset of growth of tails in the SH component, the relevant stability region being defined as that in which the energy loss to the tail generation is negligible under experimentally relevant conditions. We demonstrate that the stability domain can be readily expanded with the help of two "management" techniques (spatially periodic compensation of destabilizing effects) - the dispersion management (DM) and GVM management. In comparison with their counterparts in optical fibers, DM solitons in the chi^(2) medium feature very weak intrinsic oscillations.

physics.optics↗

arXiv2008

Gap solitons in grating superstructures

We report results of the investigation of gap solitons (GSs) in the generic model of a periodically modulated Bragg grating (BG), which includes periodic modulation of the BG chirp or local refractive index, and periodic variation of the local reflectivity. We demonstrate that, while the previously studied reflectivity modulation strongly destabilizes all solitons, the periodic chirp modulation, which is a novel feature, stabilizes a new family of double-peak fundamental BGs in the side bandgap at negative frequencies (gap No. -1), and keeps solitons stable in the central bandgap (No. 0). The two soliton families demonstrate bistability, coexisting at equal values of energy. In addition, stable 4-peak bound states are formed by pairs of fundamental GSs in bandgap -1. Self-trapping and mobility of the solitons are studied too.

nlin.PS↗

arXiv2008

Dynamics of matter-wave solitons in a time-modulated two-dimensional optical lattice

By means of the variational approximation (VA) and systematic simulations, we study dynamics and stability boundaries for solitons in a two-dimensional (2D) self-attracting Bose-Einstein condensate (BEC), trapped in an optical lattice (OL) whose amplitude is subjected to the periodic time modulation (the modulation frequency, $ω$, may be in the range of several KHz). Regions of stability of the solitons against the collapse and decay are identified in the space of the model's parameters. A noteworthy result is that the stability limit may reach the largest (100%) modulation depth, and the collapse threshold may exceed its classical value in the static lattice (which corresponds to the norm of Townes soliton). Minimum norm $% N_{\min}$ necessary for the stability of the solitons is identified too. It features a strong dependence on $ω$ at a low frequencies, due to a resonant decay of the soliton. Predictions of the VA are reasonably close to results of the simulations. In particular, the VA helps to understand salient resonant features in the shape of the stability boundaries observed with the variation of $ω$.

cond-mat.other↗

arXiv2008

Supersolitons: Solitonic excitations in atomic soliton chains

We show that, by appropriately tuning physically relevant interactions in two-component nonlinear Schrodinger equations, it is possible to achieve a regime with particle-like solitonic collisions. This allows us to construct an analogue of the Newton's cradle and also to create localized collective excitations in solitary-wave chains which are quasi-integrable solitons, i.e. supersolitons. We give a physical explanation of the phenomenon, support it with a perturbative analysis, and confirm our predictions by direct simulations.

nlin.PS↗

arXiv2008

Families of spatial solitons in a two-channel waveguide with the cubic-quintic nonlinearity

We present eight types of spatial optical solitons which are possible in a model of a planar waveguide that includes a dual-channel trapping structure and competing (cubic-quintic) nonlinearity. Among the families of trapped beams are symmetric and antisymmetric solitons of "broad" and "narrow" types, composite states, built as combinations of broad and narrow beams with identical or opposite signs ("unipolar" and "bipolar" states, respectively), and "single-sided" broad and narrow beams trapped, essentially, in a single channel. The stability of the families is investigated via eigenvalues of small perturbations, and is verified in direct simulations. Three species - narrow symmetric, broad antisymmetric, and unipolar composite states - are unstable to perturbations with real eigenvalues, while the other five families are stable. The unstable states do not decay, but, instead, spontaneously transform themselves into persistent breathers, which, in some cases, demonstrate dynamical symmetry breaking and chaotic internal oscillations. A noteworthy feature is a stability exchange between the broad and narrow antisymmetric states: in the limit when the two channels merge into one, the former species becomes stable, while the latter one loses its stability. Different branches of the stationary states are linked by four bifurcations, which take different forms in the model with the strong and weak inter-channel coupling.

nlin.PS↗

arXiv2008

Symbiotic gap and semi-gap solitons in Bose-Einstein condensates

Using the variational approximation and numerical simulations, we study one-dimensional gap solitons in a binary Bose-Einstein condensate trapped in an optical-lattice potential. We consider the case of inter-species repulsion, while the intra-species interaction may be either repulsive or attractive. Several types of gap solitons are found: symmetric or asymmetric; unsplit or split, if centers of the components coincide or separate; intra-gap (with both chemical potentials falling into a single bandgap) or inter-gap, otherwise. In the case of the intra-species attraction, a smooth transition takes place between solitons in the semi-infinite gap, the ones in the first finite bandgap, and semi-gap solitons (with one component in a bandgap and the other in the semi-infinite gap).

cond-mat.other↗

arXiv2007

Gap solitons in superfluid boson-fermion mixtures

Using coupled equations for the bosonic and fermionic order parameters, we construct families of gap solitons (GSs) in a nearly one-dimensional Bose-Fermi mixture trapped in a periodic optical-lattice (OL) potential, the boson and fermion components being in the states of the BEC and BCS superfluid, respectively. Fundamental GSs are compact states trapped, essentially, in a single cell of the lattice. Full families of such solutions are constructed in the first two bandgaps of the OL-induced spectrum, by means of variational and numerical methods, which are found to be in good agreement. The families include both intra-gap and inter-gap solitons, with the chemical potentials of the boson and fermion components falling in the same or different bandgaps, respectively.Nonfundamental states, extended over several lattice cells, are constructed too. The GSs are stable against strong perturbations.

cond-mat.other↗

arXiv2007

Fusion of necklace-ring patterns into vortex and fundamental solitons in dissipative media

We demonstrate that necklace-shaped arrays of localized spatial beams can merge into stable fundamental or vortex solitons in a generic model of laser cavities, based on the two-dimensional complex Ginzburg-Landau equation with the cubic-quintic nonlinearity. The outcome of the fusion is controlled by the number of beads in the initial necklace, 2N, and its topological charge, M. We predict and confirm by systematic simulations that the vorticity of the emerging soliton is the absolute value of difference of N and M. Threshold characteristics of the fusion are found and explained too. If the initial radius of the array (R0) is too large, it simply keeps the necklace shape (if R0 is somewhat smaller, the necklace features a partial fusion), while, if R0 is too small, the array disappears.

nlin.PS↗

arXiv2007

Matter-wave vortices in cigar-shaped and toroidal waveguides

We study vortical states in a Bose-Einstein condensate (BEC) filling a cigar-shaped trap. An effective one-dimensional (1D) nonpolynomial Schroedinger equation (NPSE) is derived in this setting, for the models with both repulsive and attractive inter-atomic interactions. Analytical formulas for the density profiles are obtained from the NPSE in the case of self-repulsion within the Thomas-Fermi approximation, and in the case of the self-attraction as exact solutions (bright solitons). A crucially important ingredient of the analysis is the comparison of these predictions with direct numerical solutions for the vortex states in the underlying 3D Gross-Pitaevskii equation (GPE). The comparison demonstrates that the NPSE provides for a very accurate approximation, in all the cases, including the prediction of the stability of the bright solitons and collapse threshold for them. In addition to the straight cigar-shaped trap, we also consider a torus-shaped configuration. In that case, we find a threshold for the transition from the axially uniform state, with the transverse intrinsic vorticity, to a symmetry-breaking pattern, due to the instability in the self-attractive BEC filling the circular trap.

cond-mat.other↗

arXiv2007

Competition between attractive and repulsive interactions in two-component Bose-Einstein condensates trapped in an optical lattice

We consider effects of inter-species attraction on two-component gap solitons (GSs) in the binary BEC with intra-species repulsion, trapped in the one-dimensional optical lattice (OL). Systematic simulations of the coupled Gross-Pitaevskii equations (GPEs) corroborate an assumption that, because the effective mass of GSs is negative, the inter-species attraction may \emph{split} the two-component soliton. Two critical values, $κ_{1} $ and $κ_{2}$, of the OL strength ($κ$) are identified. Two-species GSs with fully overlapping wave functions are stable in strong lattices ($κ>κ_{1}$). In an intermediate region, $κ_{1}>κ>κ_{2}$, the soliton splits into a double-humped state with separated components. Finally, in weak lattices ($κ<κ_{2}$%), the splitting generates a pair of freely moving single-species GSs. We present and explain the dependence of $κ_{1}$ and $κ_{2}$ on thenumber of atoms (total norm), and on the relative strength of the competing inter-species attraction and intra-species repulsion. The splitting of asymmetric solitons, with unequal norms of the two species, is briefly considered too. It is found and explained that the splitting threshold grows with the increase of the asymmetry.

cond-mat.other↗