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F. Kh. Abdullaev

Publications and source records attributed to F. Kh. Abdullaev.

At least 55 records · Page 3Linked to original sources
arXiv2007

Localized modes of binary mixtures of Bose-Einstein condensates in nonlinear optical lattices

The properties of the localized states of a two component Bose-Einstein condensate confined in a nonlinear periodic potential [nonlinear optical lattice] are investigated. We reveal the existence of new types of solitons and study their stability by means of analytical and numerical approaches. The symmetry properties of the localized states with respect to the NOL are also investigated. We show that nonlinear optical lattices allow the existence of bright soliton modes with equal symmetry in both components, bright localized modes of mixed symmetry type, as well as, dark-bright bound states and bright modes on periodic backgrounds. In spite of the quasi 1D nature of the problem, the fundamental symmetric localized modes undergo a delocalizing transition when the strength of the nonlinear optical lattice is varied. This transition is associated with the existence of an unstable solution, which exhibits a shrinking (decaying) behavior for slightly overcritical (undercritical) variations in the number of atoms.

cond-mat.other↗
arXiv2007

Collective excitations of BEC under anharmonic trap position jittering

Collective excitations of a Bose-Einstein condensate under periodic oscillations of a quadratic plus quartic trap position has been studied. A coupled set of variational equations is derived for the width and the condensate wave function center. Analytical expressions for the growth of oscillation amplitudes in the resonance case are derived. It is shown that jittering of an anharmonic trap position can cause double resonance of the BEC width and the center of mass oscillation in the wide range of the BEC parameters values. The predictions of variational approach are confirmed by full numerical simulations of the 1D GP equation.

cond-mat.other↗
arXiv2007

Generalized Neighbor-Interaction Models Induced by Nonlinear Lattices

It is shown that the tight-binding approximation of the nonlinear Schrödinger equation with a periodic linear potential and periodic in space nonlinearity coefficient gives rise to a number of nonlinear lattices with complex, both linear and nonlinear, neighbor interactions. The obtained lattices present non-standard possibilities, among which we mention a quasi-linear regime, where the pulse dynamics obeys essentially the linear Schr{ö}dinger equation. We analyze the properties of such models both in connection with their modulational stability, as well as in regard to the existence and stability of their localized solitary wave solutions.

cond-mat.other↗
arXiv2007

Dissipative Dynamics of Matter Wave Soliton in Nonlinear Optical Lattice

Dynamics and stability of solitons in two-dimensional (2D) Bose-Einstein condensates (BEC), with low-dimensional (1D) conservative plus dissipative nonlinear optical lattices are investigated. In the case of focusing media (with attractive atomic systems) the collapse of the wave packet is arrested by the dissipative periodic nonlinearity. The adiabatic variation of the background scattering length leads to metastable matter-wave solitons. When the atom feeding mechanism is used, a dissipative soliton can exist in focusing 2D media with 1D periodic nonlinearity. In the defocusing media (repulsive BEC case) with harmonic trap in one dimension and one dimensional nonlinear optical lattice in other direction, the stable soliton can exist. This prediction of variational approach is confirmed by the full numerical simulation of 2D Gross-Pitaevskii equation.

cond-mat.other↗
arXiv2006

Discrete breathers in BEC with two- and three-body interactions in optical lattice

We investigate the properties of discrete breathers in a Bose-Einstein condensate with two- and three-body interactions in optical lattice. In the tight-binding approximation the Gross-Pitaevskii equation with periodic potential for the condensate wavefunction is reduced to the cubic-quintic discrete nonlinear Schrödinger equation. We analyze the regions of modulational instabilities of nonlinear plane waves. This result is important to obtain the conditions for generation of discrete solitons(breathers) in optical lattice. Also using the Page approach, we derive the conditions for the existence and stability for bright discrete breather solutions. It is shown that the quintic nonlinearity brings qualitatively new conditions for stability of strongly localized modes. The numerical simulations conform with the analytical predictions.

cond-mat.other↗
arXiv2004

Collective oscillations of one-dimensional Bose-Einstein gas in a time-varying trap potential and atomic scattering length

The collective oscillations of 1D repulsive Bose gas with external harmonic confinement in two different regimes are studied. The first regime is the mean field regime when the density is high. The second regime is the Tonks-Girardeau regime when the density is low. We investigate the resonances under periodic modulations of the trap potential and the effective nonlinearity. Modulations of the effective nonlinear coefficient result from modulations of the atomic scattering length by the Feshbach resonance method or variations of the transverse trap frequency. In the mean field regime we predict the bistability in the nonlinear oscillations of the condensate. In the Tonks-Girardeau regime the resonance has the character of a linear parametric resonance. In the case of rapid strong modulations of the nonlinear coefficient we find analytical expressions for the nonlinearity managed soliton width and the frequency of the slow secondary oscillations near the fixed point.

cond-mat.other↗
arXiv2004

Symmetry breaking induced by random fluctuations for Bose-Einstein condensates in a double-well trap

This paper is devoted to the study of the dynamics of two weakly-coupled Bose-Einstein condensates confined in a double-well trap and perturbed by random external forces. Energy diffusion due to random forcing allows the system to visit symmetry-breaking states when the number of atoms exceeds a threshold value. The energy distribution evolves to a stationary distribution which depends on the initial state of the condensate only through the total number of atoms. This loss of memory of the initial conditions allows a simple and complete description of the stationary dynamics of the condensate which randomly visits symmetric and symmetry-breaking states.

cond-mat.other↗
arXiv2004

Collapse of a Bose-Einstein condensate induced by fluctuations of the laser intensity

The dynamics of a metastable attractive Bose-Einstein condensate trapped by a system of laser beams is analyzed in the presence of small fluctuations of the laser intensity. It is shown that the condensate will eventually collapse. The expected collapse time is inversely proportional to the integrated covariance of the time autocorrelation function of the laser intensity and it decays logarithmically with the number of atoms. Numerical simulations of the stochastic 3D Gross-Pitaevskii equation confirms analytical predictions for small and moderate values of mean field interaction.

cond-mat.soft↗
arXiv2004

Optical pulse propagation in fibers with random dispersion

The propagation of optical pulses in two types of fibers with randomly varying dispersion is investigated. The first type refers to a uniform fiber dispersion superimposed by random modulations with a zero mean. The second type is the dispersion-managed fiber line with fluctuating parameters of the dispersion map. Application of the mean field method leads to the nonlinear Schrödinger equation (NLSE) with a dissipation term, expressed by a 4th order derivative of the wave envelope. The prediction of the mean field approach regarding the decay rate of a soliton is compared with that of the perturbation theory based on the Inverse Scattering Transform (IST). A good agreement between these two approaches is found. Possible ways of compensation of the radiative decay of solitons using the linear and nonlinear amplification are explored. Corresponding mean field equation coincides with the complex Swift-Hohenberg equation. The condition for the autosolitonic regime in propagation of optical pulses along a fiber line with fluctuating dispersion is derived and the existence of autosoliton (dissipative soliton) is confirmed by direct numerical simulation of the stochastic NLSE. The dynamics of solitons in optical communication systems with random dispersion-management is further studied applying the variational principle to the mean field NLSE, which results in a system of ODE's for soliton parameters. Extensive numerical simulations of the stochastic NLSE, mean field equation and corresponding set of ODE's are performed to verify the predictions of the developed theory.

nlin.PS↗
arXiv2003

Formation of soliton trains in Bose-Einstein condensates as a nonlinear Fresnel diffraction of matter waves

The problem of generation of atomic soliton trains in elongated Bose-Einstein condensates is considered in framework of Whitham theory of modulations of nonlinear waves. Complete analytical solution is presented for the case when the initial density distribution has sharp enough boundaries. In this case the process of soliton train formation can be viewed as a nonlinear Fresnel diffraction of matter waves. Theoretical predictions are compared with results of numerical simulations of one- and three-dimensional Gross-Pitaevskii equation and with experimental data on formation of Bose-Einstein bright solitons in cigar-shaped traps.

cond-mat.soft↗
arXiv2003

Adiabatic Compression of Soliton Matter Waves

The evolution of atomic solitary waves in Bose-Einstein condensate (BEC) under adiabatic changes of the atomic scattering length is investigated. The variations of amplitude, width, and velocity of soliton are found for both spatial and time adiabatic variations. The possibility to use these variations to compress solitons up to very high local matter densities is shown both in absence and in presence of a parabolic confining potential.

cond-mat↗
arXiv2003

Array of Bose-Einstein condensates under time-periodic Feshbach-resonance management

The dynamics of a discrete soliton in an array of Bose-Einstein condensates under the action of a periodically time-modulated atomic scattering length (``Feshbach-resonance management, FRM'') is investigated. The cases of both slow and rapid modulation, in comparison with the tunneling frequency, are considered. We employ a discrete variational approach for the analysis of the system. The existence of nonlinear resonances and chaos is predicted at special values of the driving frequency. Soliton splitting is observed in numerical simulations. In the case of the rapid modulation, we derive an averaged equation, which is a generalized discrete nonlinear Schroedinger equation, including higher-order effective nonlinearities and intersite nonlinear interactions. Thus the predicted discrete FRM solitons are a direct matter-wave analog of recently investigated discrete diffraction-managed optical solitons.

cond-mat.soft↗
arXiv2003

Stable two-dimensional dispersion-managed soliton

The existence of a dispersion-managed soliton in two-dimensional nonlinear Schrödinger equation with periodically varying dispersion has been explored. The averaged equations for the soliton width and chirp are obtained which successfully describe the long time evolution of the soliton. The slow dynamics of the soliton around the fixed points for the width and chirp are investigated and the corresponding frequencies are calculated. Analytical predictions are confirmed by direct PDE and ODE simulations. Application to a Bose-Einstein condensate in optical lattice is discussed. The existence of a dispersion-managed matter-wave soliton in such system is shown.

cond-mat.soft↗
arXiv2003

Interaction of pulses in nonlinear Schroedinger model

The interaction of two rectangular pulses in nonlinear Schroedinger model is studied by solving the appropriate Zakharov-Shabat system. It is shown that two real pulses may result in appearance of moving solitons. Different limiting cases, such as a single pulse with a phase jump, a single chirped pulse, in-phase and out-of-phase pulses, and pulses with frequency separation, are analyzed. The thresholds of creation of new solitons and multi-soliton states are found.

nlin.PS↗
arXiv2002

Dynamics of bright matter-wave solitons in inhomogeneous cigar-type Bose-Einstein condensate

We discuss the possible observation of a new type of standing nonlinear atomic matter wave in the condensate: the nonlinear impurity mode. It is investigated dynamical effects of a bright soliton in Bose-Einstein-condensed (BEC) systems with local space variations of the two-body atomic scattering length. A rich dynamics is observed in the interaction between the soliton and an inhomogeneity. Processes as trapping, reflection and transmission of the bright matter soliton due to the impurity are studied considering an analytical time-dependent variational approach and also by full numerical simulation. A condition is obtained for the collapse of the bright solitary wave in the quasi-one-dimensional BEC with attractive local inhomogeneity.

cond-mat.soft↗
arXiv2002

Controlling collapse in Bose-Einstein condensates by temporal modulation of the scattering length

We consider, by means of the variational approximation (VA) and direct numerical simulations of the Gross-Pitaevskii (GP) equation, the dynamics of 2D and 3D condensates with a scattering length containing constant and harmonically varying parts, which can be achieved with an ac magnetic field tuned to the Feshbach resonance. For a rapid time modulation, we develop an approach based on the direct averaging of the GP equation,without using the VA. In the 2D case, both VA and direct simulations, as well as the averaging method, reveal the existence of stable self-confined condensates without an external trap, in agreement with qualitatively similar results recently reported for spatial solitons in nonlinear optics. In the 3D case, the VA again predicts the existence of a stable self-confined condensate without a trap. In this case, direct simulations demonstrate that the stability is limited in time, eventually switching into collapse, even though the constant part of the scattering length is positive (but not too large). Thus a spatially uniform ac magnetic field, resonantly tuned to control the scattering length, may play the role of an effective trap confining the condensate, and sometimes causing its collapse.

cond-mat↗
arXiv2002

Dynamics of bright matter wave solitons in a quasi 1D Bose-Einstein condensate with a rapidly varying trap

The dynamics of a bright matter wave soliton in a quasi 1D Bose-Einstein condensate with periodically rapidly varying trap is considered. The governing equation is derived based on averaging over fast modulations of the Gross-Pitaevskii (GP) equation. This equation has the form of GP equation with effective potential of more complicated structure than unperturbed trap. For the case of inverted (expulsive) quadratic trap corresponding to unstable GP equation, the effective potential can be stable. For the bounded in space trap potential it is showed that the bifurcation exists, i.e.,the single well potential bifurcates to the triple well effective potential. Stabilization of BEC cloud on-site state in the temporary modulated optical lattice is found. (analogous to the Kapitza stabilization of the pendulum). The predictions of the averaged GP equation are confirmed by the numerical simulations of GP equation with rapid perturbations.

cond-mat.soft↗