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Jurnal pengukuran kualiti dan analisis/Journal of Quality Measurement and Analysis

Compactons in Interspecies Spin-Orbit-Coupled Nonlinear Schrödinger Lattices Under Strong Nonlinearity Management

Published Jul 22, 2024• 0 citations
Publisher

Abstract

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.

DOI
10.17576/jqma.2002.2024.09

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•Jan 1, 2013•0 citations
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.
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.
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.
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.
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.
Lattice Compactons, discrete breathers with compact support, were found for a discrete nonlinear Schrodinger (DNLS) equation extended with nearest neighbour intersite nonlinearities [1], a model originally studied with waveguide arrays in mind. These compactons were shown to exhibit very good mobility if the parameters are tuned close to the compactons stability boundary. The DNLS can also be used to model the behaviour of Bose-Einstein condensates in optical lattices, and the remarkable control over the experiments in this field of research has made it possible to study the quantum mechanics of strongly correlated atoms.We will define the concept of a Quantum Lattice Compacton [2] and discuss the existence and dynamics, with special emphasis on mobility [3], of these in an extended Bose-Hubbard model corresponding to above-mentioned extended DNLS equation in the quantum mechanical limit. The compactons is given 'a kick' by means of a phase-gradient and it is shown that the size of this phase is crucial for the mobility of the compactons. For small phase-gradients, corresponding to a slow coherent motion in the classical model, the time-scales of the quantum tunnelings become of the same order as the time-scale of the translational motion and the classical mobility is destroyed by quantum fluctuations. For large phase-gradients, corresponding to rapid classical motion, the classical and quantum time-scales separate so that a mobile, localized coherent quantum state can be translated many sites in the lattice already for small particle numbers of the order of 10 [3].Acknowledgements: This project has been financed by the Swedish Research Council.References[1] M. Oster, M. Johansson, and A. Eriksson 2003 Phys. Rev. E 67 056606[2] P. Jason and M. Johansson 2012 Phys. Rev. A 85 011603(R)[3] P. Jason and M. Johansson 2013 Phys. Rev. A 88 033605