Two-dimensional discrete solitons in dipolar Bose-Einstein condensates

We analyze the formation and dynamics of bright unstaggered solitons in the disk-shaped dipolar Bose-Einstein condensate, which features the interplay of contact (collisional) and long-range dipole-dipole (DD) interactions between atoms. The condensate is assumed to be trapped in a strong optical-lattice potential in the disk's plane, hence it may be approximated by a two-dimensional (2D) discrete model, which includes the on-site nonlinearity and cubic long-range (DD) interactions between sites of the lattice. We consider two such models, that differ by the form of the on-site nonlinearity, represented by the usual cubic term, or more accurate nonpolynomial one, derived from the underlying 3D Gross-Pitaevskii equation. Similar results are obtained for both models. The analysis is focused on effects of the DD interaction on fundamental localized modes in the lattice (2D discrete solitons). The repulsive isotropic DD nonlinearity extends the existence and stability regions of the fundamental solitons. New families of on-site, inter-site and hybrid solitons, built on top of a finite background, are found as a result of the interplay of the isotropic repulsive DD interaction and attractive contact nonlinearity. By themselves, these solutions are unstable, but they evolve into robust breathers which exist on an oscillating background. In the presence of the repulsive contact interactions, fundamental localized modes exist if the DD interaction (attractive isotropic or anisotropic) is strong enough. They are stable in narrow regions close to the anticontinuum limit, while unstable solitons evolve into breathers. In the latter case, the presence of the background is immaterial

Solitons in combined linear and nonlinear lattice potentials

We study ordinary solitons and gap solitons (GSs) in the effectively one-dimensional Gross-Pitaevskii equation, with a combination of linear and nonlinear lattice potentials. The main points of the analysis are effects of the (in)commensurability between the lattices, the development of analytical methods, viz., the variational approximation (VA) for narrow ordinary solitons, and various forms of the averaging method for broad solitons of both types, and also the study of mobility of the solitons. Under the direct commensurability (equal periods of the lattices, the family of ordinary solitons is similar to its counterpart in the free space. The situation is different in the case of the subharmonic commensurability, with L_{lin}=(1/2)L_{nonlin}, or incommensurability. In those cases, there is an existence threshold for the solitons, and the scaling relation between their amplitude and width is different from that in the free space. GS families demonstrate a bistability, unless the direct commensurability takes place. Specific scaling relations are found for them too. Ordinary solitons can be readily set in motion by kicking. GSs are mobile too, featuring inelastic collisions. The analytical approximations are shown to be quite accurate, predicting correct scaling relations for the soliton families in different cases. The stability of the ordinary solitons is fully determined by the VK (Vakhitov-Kolokolov) criterion, while the stability of GS families follows an inverted ("anti-VK") criterion, which is explained by means of the averaging approximation.Comment: 9 pages, 6 figure

Deviation from one-dimensionality in stationary properties and collisional dynamics of matter-wave solitons

By means of analytical and numerical methods, we study how the residual three-dimensionality affects dynamics of solitons in an attractive Bose-Einstein condensate loaded into a cigar-shaped trap. Based on an effective 1D Gross-Pitaevskii equation that includes an additional quintic self-focusing term, generated by the tight transverse confinement, we find a family of exact one-soliton solutions and demonstrate stability of the entire family, despite the possibility of collapse in the 1D equation with the quintic self-focusing nonlinearity. Simulating collisions between two solitons in the same setting, we find a critical velocity, $V_{c}$, below which merger of identical in-phase solitons is observed. Dependence of $V_{c}$ on the strength of the transverse confinement and number of atoms in the solitons is predicted by means of the perturbation theory and investigated in direct simulations. Symmetry breaking in collisions of identical solitons with a nonzero phase difference is also shown in simulations and qualitatively explained by means of an analytical approximation.Comment: 10 pages, 7 figure

Changes in the indicators of cardiac pumping function of parachutists before jumping and after landing

© 2016, International Journal of Pharmacy and Technology. All rights reserved.Studying the reaction of the cardiac pumping function of the parachutists at various stages of preparation for jump, we found that, as the athletes develop their skills, the difference between the values of heart rate prior to and after landing decreases significantly. At the same time, the least difference in heart rate values prior to and after landing was recorded in the masters of sports of international class. While the athletes of participation classes and masters of sports have this difference maintained at a high level of nearly 69-70 bpm (P <0.05). The maximum difference in heart rate values prior to and after landing was recorded in ex-masters of sports. As the parachutists upgrade their level of fitness, the stroke volume response, on the contrary, increases. However, we detected a negative stroke volume response for the first time in both the beginners and the ex-masters of sports after the jump

Relative localization for aerial manipulation with PL-SLAM

The final publication is available at link.springer.comThis chapter explains a precise SLAM technique, PL-SLAM, that allows to simultaneously process points and lines and tackle situations where point-only based methods are prone to fail, like poorly textured scenes or motion blurred images where feature points are vanished out. The method is remarkably robust against image noise, and that it outperforms state-of-the-art methods for point based contour alignment. The method can run in real-time and in a low cost hardware.Peer ReviewedPostprint (author's final draft

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).Comment: 5 pages, 9 figure

Bright vector solitons in cross-defocusing nonlinear media

We study two-dimensional soliton-soliton vector pairs in media with self-focusing nonlinearities and defocing cross-interactions. The general properties of the stationary states and their stability are investigated. The different scenarios of instability are observed using numerical simulations. The quasi-stable propagation regime of the high-power vector solitons is revealed.Comment: 6 pages, 7 figure

Photon-Number-Splitting versus Cloning Attacks in Practical Implementations of the Bennett-Brassard 1984 protocol for Quantum Cryptography

In practical quantum cryptography, the source sometimes produces multi-photon pulses, thus enabling the eavesdropper Eve to perform the powerful photon-number-splitting (PNS) attack. Recently, it was shown by Curty and Lutkenhaus [Phys. Rev. A 69, 042321 (2004)] that the PNS attack is not always the optimal attack when two photons are present: if errors are present in the correlations Alice-Bob and if Eve cannot modify Bob's detection efficiency, Eve gains a larger amount of information using another attack based on a 2->3 cloning machine. In this work, we extend this analysis to all distances Alice-Bob. We identify a new incoherent 2->3 cloning attack which performs better than those described before. Using it, we confirm that, in the presence of errors, Eve's better strategy uses 2->3 cloning attacks instead of the PNS. However, this improvement is very small for the implementations of the Bennett-Brassard 1984 (BB84) protocol. Thus, the existence of these new attacks is conceptually interesting but basically does not change the value of the security parameters of BB84. The main results are valid both for Poissonian and sub-Poissonian sources.Comment: 11 pages, 5 figures; "intuitive" formula (31) adde

Universal fractal structures in the weak interaction of solitary waves in generalized nonlinear Schr\"{o}dinger equations

Weak interactions of solitary waves in the generalized nonlinear Schr\"{o}dinger equations are studied. It is first shown that these interactions exhibit similar fractal dependence on initial conditions for different nonlinearities. Then by using the Karpman-Solov'ev method, a universal system of dynamical equations is derived for the velocities, amplitudes, positions and phases of interacting solitary waves. These dynamical equations contain a single parameter, which accounts for the different forms of nonlinearity. When this parameter is zero, these dynamical equations are integrable, and the exact analytical solutions are derived. When this parameter is non-zero, the dynamical equations exhibit fractal structures which match those in the original wave equations both qualitatively and quantitatively. Thus the universal nature of fractal structures in the weak interaction of solitary waves is analytically established. The origin of these fractal structures is also explored. It is shown that these structures bifurcate from the initial conditions where the solutions of the integrable dynamical equations develop finite-time singularities. Based on this observation, an analytical criterion for the existence and locations of fractal structures is obtained. Lastly, these analytical results are applied to the generalized nonlinear Schr\"{o}dinger equations with various nonlinearities such as the saturable nonlinearity, and predictions on their weak interactions of solitary waves are made.Comment: 22pages, 15 figure

Matter-wave 2D solitons in crossed linear and nonlinear optical lattices

It is demonstrated the existence of multidimensional matter-wave solitons in a crossed optical lattice (OL) with linear OL in the $x-$direction and nonlinear OL (NOL) in the $y-$direction, where the NOL can be generated by a periodic spatial modulation of the scattering length using an optically induced Feshbach resonance. In particular, we show that such crossed linear and nonlinear OL allows to stabilize two-dimensional (2D) solitons against decay or collapse for both attractive and repulsive interactions. The solutions for the soliton stability are investigated analytically, by using a multi-Gaussian variational approach (VA), with the Vakhitov-Kolokolov (VK) necessary criterion for stability; and numerically, by using the relaxation method and direct numerical time integrations of the Gross-Pitaevskii equation (GPE). Very good agreement of the results corresponding to both treatments is observed.Comment: 8 pages (two-column format), with 16 eps-files of 4 figure