arXiv subjects

F. Kh. Abdullaev

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

62 records · Page 4Linked to original sources

arXiv2002

Dynamics of a trapped 2D Bose-Einstein condensate with periodically and randomly varying atomic scattering length

In this work we consider the oscillations and associated resonance of a 2D Bose-Einstein condensate under periodic and random modulations of the atomic scattering length. For random oscillations of the trap potential and of the atomic scattering length we are able to calculate the mean growth rate for the width of the condensate. The results obtained from the reduced ODE's for oscillations of the width of condensate are compared with the numerical simulations of the full 2D Gross-Pitaevskii equation with modulated in time coefficients.

cond-mat.soft↗

arXiv2001

Nonlinear excitations in arrays of Bose-Einstein condensates

The dynamics of localized excitations in array of Bose-Einstein condensates is investigated in the framework of the nonlinear lattice theory. The existence of temporarily stable ground states displaying an atomic population distributions localized on very few lattice sites (intrinsic localized modes), as well as, of atomic population distributions involving many lattice sites (envelope solitons), is studied both numerically and analytically. The origin and properties of these modes are shown to be inherently connected with the interplay between macroscopic quantum tunnelling and nonlinearity induced self-trapping of atoms in coupled BECs. The phenomenon of Bloch oscillations of these excitations is studied both for zero and non zero backgrounds. We find that in a definite range of parameters, homogeneous distributions can become modulationally unstable. We also show that bright solitons and excitations of shock wave type can exist in BEC arrays even in the case of positive scattering length. Finally, we argue that BEC array with negative scattering length in presence of linear potentials can display collapse.

cond-mat.soft↗

arXiv2001

Dynamics of a Bose-Einstein condensate in optical trap

The dynamics of a 2D Bose-Einstein condensate in optical trap is studied taking into consideration fluctuations of the far-off-resonance laser field intensity. The problem is described in the frame of the mean field Gross-Pitaevskii equation with randomly varying trap potential. An analytic approach based on the moments method has been employed to describe the noise induced evolution of the condensate properties. Stochastic parametric resonance in oscillations of the condensate width is proved to exist. For the condensate with negative scattering length of atoms, it is shown that the noise can delay or even arrest the collapse. Analytical predictions are confirmed by numerical simulations of the underlying PDE and ODE models.

cond-mat.soft↗

arXiv2001

Stability of trapped Bose-Einstein condensates

In three-dimensional trapped Bose-Einstein condensate (BEC), described by the time-dependent Gross-Pitaevskii-Ginzburg equation, we study the effect of initial conditions on stability using a Gaussian variational approach and exact numerical simulations. We also discuss the validity of the criterion for stability suggested by Vakhitov and Kolokolov. The maximum initial chirp (initial focusing defocusing of cloud) that can lead a stable condensate to collapse even before the number of atoms reaches its critical limit is obtained for several specific cases. When we consider two- and three-body nonlinear terms, with negative cubic and positive quintic terms, we have the conditions for the existence of two phases in the condensate. In this case, the magnitude of the oscillations between the two phases are studied considering sufficient large initial chirps. The occurrence of collapse in a BEC with repulsive two-body interaction is also shown to be possible.

cond-mat.soft↗

arXiv2000

Autosolitons in trapped Bose-Einstein condensates with two- and three-body inelastic processes

In this work, we consider the conditions for the existence of autosolitons, in trapped Bose-Einstein condensates with attractive atomic interactions. First, the variational approach is employed to estimate the stationary solutions for the three-dimensional Gross-Pitaevskii equation with trap potential, linear atomic feeding from the thermal cloud and two- and three-body inelastic processes. Next, by using exact numerical calculations, we show that the variational approach gives reliable analytical results. We also discuss the possible observation of autosolitons in experiments with Lithium-7.

cond-mat.soft↗

arXiv2000

Macroscopic quantum tunneling and resonances in coupled Bose-Einstein condensates with oscillating atomic scattering length

We study the macroscopic quantum tunneling, self-trapping phenomena in two weakly coupled Bose-Einstein condensates with periodically time-varying atomic scattering length. The resonances in the oscillations of the atomic populations are investigated. We consider oscillations in the cases of macroscopic quantum tunneling and the self-trapping regimes. The existence of chaotic oscillations in the relative atomic population due to overlaps between nonlinear resonances is showed. We derive the whisker-type map for the problem and obtain the estimate for the critical amplitude of modulations leading to chaos. The diffusion coefficient for motion in the stochastic layer near separatrix is calculated. The analysis of the oscillations in the rapidly varying case shows the possibilty of stabilization of the unstable Pi-mode regime.

cond-mat.soft↗

arXiv2000

Coherent Atomic Oscillations and Resonances between Coupled Bose-Einstein Condensates with Time-Dependent Trapping Potential

We study the quantum coherent-tunneling between two Bose-Einstein condensates separated through an oscillating trap potential. The cases of slowly and rapidly varying in time trap potential are considered. In the case of a slowly varying trap we study the nonlinear resonances and chaos in the oscillations of the relative atomic population. Using the Melnikov function approach, we find the conditions for chaotic macroscopic quantum-tunneling phenomena to exists. Criteria for the onset of chaos are also given. We find the values of frequency and modulation amplitude which lead to chaos on oscillations in the relative population, for any given damping and the nonlinear atomic interaction. In the case of a rapidly varying trap we use the multiscale expansion method in the parameter epsilon = 1/Omega, where Omega is the frequency of modulations and we derive the averaged system of equations for the modes. The analysis of this system shows that new macroscopic quantum self trapping regions, in comparison with the constant trap case, exist.

cond-mat.soft↗

arXiv2000

Stability analysis of the D-dimensional nonlinear Schroedinger equation with trap and two- and three-body interactions

Considering the static solutions of the D-dimensional nonlinear Schroedinger equation with trap and attractive two-body interactions, the existence of stable solutions is limited to a maximum critical number of particles, when D is greater or equal 2. In case D=2, we compare the variational approach with the exact numerical calculations. We show that, the addition of a positive three-body interaction allows stable solutions beyond the critical number. In this case, we also introduce a dynamical analysis of the conditions for the collapse.

cond-mat.soft↗