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Photonics and Fiber Technology Congress (ACOFT, BGPP, NP)

Compactons of Binary Bose Gases in Optical Lattices with Inter-species Scattering Length Management

F. Kh. Abdullaev, M. S. A. Hadi, Mario Salerno, Bakhram Umarov

Published Jan 1, 2016• 0 citations
Publisher

Abstract

Binary mixtures of quasi one-dimensional Bose-Einstein condensates (BEC) in deep optical lattices and in the presence of periodic rapid modulations of the interspecies scattering length are investigated. In the strong management limit the existence of binary compactons of stationary and quasi-stationary type is demonstrated. The existence of a threshold on the inter-species scattering length in the case of quasi-stationary compactons is shown.

DOI
10.1364/acoft.2016.jt4a.14

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Binary mixtures of quasi one-dimensional Bose-Einstein condensates (BEC) in deep optical lattices and in the presence of periodic rapid modulations of the interspecies scattering length are investigated. In the strong management limit the existence of binary compactons of stationary and quasi-stationary type is demonstrated. The existence of a threshold on the inter-species scattering length in the case of quasi-stationary compactons is shown.
Abstract Binary mixtures of quasi one-dimensional Bose–Einstein condensates (BECs) trapped in deep optical lattices (OLs) in the presence of periodic time modulations of the inter-species scattering length are investigated. We adopt a mean field description and use the tight-binding approximation and averaging method to derive averaged model equations in the form of two coupled discrete nonlinear Schrödinger equations (DNLSEs) with tunneling constants that nonlinearly depend on inter-species coupling. We show that for strong and rapid modulations of the inter-species scattering length, the averaged system admits exact compacton solutions, e.g. solutions that have no tails and are fully localized on a compact which is achieved when the densities at the compact edges are in correspondence with zeros of the Bessel function (zero tunneling condition). Deviations from exact conditions give rise to the formation of quasi-compactons, e.g. non-exact excitations which look like compactons for any practical purpose, for which the zero tunneling condition is achieved dynamically thanks to an effective nonlinear dispersive coupling induced by scattering length modulation. The stability properties of compactons and quasi-compactons are investigated by linear analysis and numerical integrations of the averaged system, respectively, and the results are compared with those of the original time dependent driven system. In particular, the occurrence of delocalizing transitions with the existence of thresholds in the mean inter-species scattering length is explicitly demonstrated. Under proper management conditions, stationary compactons and quasi-compactons are quite stable and robust excitations that can survive on a very long time scale. A parameter design and a possible experimental setting for the observation of these excitations are briefly discussed.
The existence of compacton matter waves in binary mixtures of quasi-one-dimensional Bose-Einstein condensates in deep optical lattices, and in the presence of nonlinearity management, is demonstrated. For this, we derive an averaged vector discrete nonlinear Schr\"odinger equation (DNLSE) and show that compacton solutions of different types can exist as stable excitations. Stability properties are studied by linear analysis and by direct numerical integrations of the DNLSE system and their dependence on the inter- and intraspecies scattering lengths investigated. We show that under proper management conditions, compactons can be very robust excitations that can emerge spontaneously from generic initial conditions. A possible experimental setting for compacton observation is also discussed.
Compacton matter waves are considered in Bose-Einstein condensates (BEC) and in binary BEC mixtures, trapped in deep optical lattices in the presence of strong and rapid periodic time modulations of the atomic scattering length, are considered.For this, we derive vector averaged discrete nonlinear Schrödinger equations (DNLSE) and show that compacton solutions of different types can exist as stable excitations.Stability properties are studied by linear analysis and by direct numerical integrations of the DNLSE system.
We demonstrate the existence of compactons matter waves in binary mixtures of Bose-Einstein condensates (BEC) trapped in deep optical lattices (OL) subjected to equal contributions of intraspecies Rashba and Dresselhaus spin-orbit coupling (SOC) under periodic time modulations of the intraspecies scattering length. We show that these modulations lead to a rescaling of the SOC parameters that involves the density imbalance of the two components. This gives rise to density dependent SOC parameters that strongly influence the existence and the stability of compacton matter waves. The stability of SOC-compactons is investigated both by linear stability analysis and by time integrations of the coupled Gross-Pitaevskii equations. We find that SOC restricts the parameter ranges for stable stationary SOC-compacton existence but, on the other side, it gives a more stringent signature of their occurrence. In particular, SOC-compactons should appear when the intraspecies interactions and the number of atoms in the two components are perfectly balanced (or close to being balanced for the metastable case). The possibility to use SOC-compactons as a tool for indirect measurements of the number of atoms and/or the intraspecies interactions is also suggested.
This study shows the existence of special matter waves, known as compactons, in binary discrete nonlinear Schrödinger (DNLS) equations with equal distributions of interspecies Rashba and Dresselhaus spin-orbit coupling (SOC) in the presence of fast periodic time modulations of the interspecies scattering length.However, the existence is limited to only of one-site compacton type, which means the absence of larger size compactons such as the two-and three-site.Further, the dynamical stability of the compactons is predicted by using linear stability analysis method and verified through the direct numerical integrations of the equations.We find that the stability of the compactons has strong dependence on the strength of SOC term.
Superfluid properties of Bose-Einstein condensates (BEC) in toroidal quasi-one-dimensional traps are investigated in the presence of periodic scattering length modulations along the ring. The existence of several types of stable periodic waves, ranging from almost uniform to very fragmented chains of weakly interacting and equally spaced solitons, is demonstrated. We show that these waves may support persistent atomic currents and sound waves with spectra of Bogoliubov type. Fragmented condensates can be viewed as arrays of Josephson junctions and the current as a BEC manifestation of the dc-Josephson effect. The influence of linear defects on BEC superfluidity has been also investigated. We found that for subcritical velocities, linear defects that are static with respect to the lattice (while the condensate moves in respect to both the optical lattice and the defect) preserve the BEC superfluidity.