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Peakons in spinor F=1 Bose–Einstein condensates with PT-symmetric δ-function potentials

Lao, Jun-Yi, Qin, Zi-Yang, Zhang, Jia-Rui, Shen, Yu-Jia

Published Jan 1, 2024• 0 citations
OpenAlex

Abstract

By introducing PT-symmetric δ-function potentials into three-component Gross–Pitaevskii equations that describe spinor F=1 Bose–Einstein condensates, we obtain stable and unstable analytical peakon solutions which enable us to explore the patterns of mean-field and spin-exchange interaction in relation to variations in energy of nonlinear modes. Furthermore, using iterative algorithms, we generate a series of numerical solutions and represent several families of peakon solutions in the form of energy curves, examining the impact of parameters on energy. Additionally, we observe a closed-loop structure in the family of peakons, with P0 and μ0 serving as the coordinate axes. On this curve, we discover stable peakons exhibiting periodic oscillatory properties, which can be regarded as a form of internal energy transfer within the coupled system. This research could contribute to a more comprehensive understanding of coupled nonlinear systems and serve as a reference for future experiments in this domain.

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By introducing PT-symmetric δ-function potentials into three-component Gross–Pitaevskii equations that describe spinor F=1 Bose–Einstein condensates, we obtain stable and unstable analytical peakon solutions which enable us to explore the patterns of mean-field and spin-exchange interaction in relation to variations in energy of nonlinear modes. Furthermore, using iterative algorithms, we generate a series of numerical solutions and represent several families of peakon solutions in the form of energy curves, examining the impact of parameters on energy. Additionally, we observe a closed-loop structure in the family of peakons, with P0 and μ0 serving as the coordinate axes. On this curve, we discover stable peakons exhibiting periodic oscillatory properties, which can be regarded as a form of internal energy transfer within the coupled system. This research could contribute to a more comprehensive understanding of coupled nonlinear systems and serve as a reference for future experiments in this domain.
Abstract Introducing P T -symmetric generalized Scarf-II potentials into the three-coupled nonlinear Gross–Pitaevskii equations offers a new way to seek stable soliton states in quasi-one-dimensional spin-1 Bose–Einstein condensates. In scenarios where the spin-independent parameter c 0 and the spin-dependent parameter c 2 vary, we use both analytical and numerical methods to investigate the three-coupled nonlinear Gross–Pitaevskii equations with P T -symmetric generalized Scarf-II potentials. We obtain analytical soliton states and find that simply modulating c 2 may change the analytical soliton states from unstable to stable. Additionally, we obtain numerically stable double-hump soliton states propagating in the form of periodic oscillations, exhibiting distinct behavior in energy exchange. For further investigation, we discuss the interaction of numerical double-hump solitons with Gaussian solitons and observe the transfer of energy among the three components. These findings may contribute to a deeper understanding of solitons in Bose–Einstein condensates with P T -symmetric potentials and may hold significance for both theoretical understanding and experimental design in related physics experiments.
We investigate the different types of matter-wave solitons in spin-orbit-coupled spin-2 spinor Bose-Einstein condensates. Using mean-field theory and adopting the multiscale perturbation method, the original five-component Gross-Pitaevskii spin-orbit-coupled spin-2 spinor Bose-Einstein condensate model can be reduced to a single effective nonlinear Schrödinger equation, which allows us to find analytical soliton solutions of this system. In this way, for different regimes of the spin-orbit coupling, Raman coupling, and interatomic interactions, we find approximate bright and dark soliton solutions. Particularly, the type of solitons depends on the dispersion properties of the system. When the lowest-energy band has a single-well structure, we find there only exist positive mass bright or dark solitons due to the dispersion coefficient of effective nonlinear Shrödinger equation always positive. However, when the lowest-energy band has a double-well structure, there will appear positive (negative) mass bright or dark solitons because the sign of the dispersion coefficient can be positive (negative) under different momentum. We employ direct numerical simulation of the original five-component Gross-Pitaevskii equations to confirm the analytical results.
We propose a method to analytically solve the one-dimensional coupled nonlinear Gross-Pitaevskii equations which govern the motion of the spinor Bose-Einstein condensates. In a uniform external potential, the Hamiltonian comprises the kinetic energy, the linear and the quadratic Zeeman energies. Several classes of exact periodic and solitonic solutions, either in real or in complex forms, are obtained for both the F=1 and F=2 condensates. These solutions are general that contain neither approximations nor constraints on the system parameters.
Abstract The existence and stability of gap solitons in a quasi-one-dimensional Bose–Einstein condensate with three-body interactions loaded in a PT-symmetric potential are investigated numerically. Under the mean-field approximation, the dynamical behaviors of the system are described by a cubic-quintic Gross–Pitaevskii equation. Firstly, we obtained the band-gap structures via linearizing the GPE. The PT-symmetric of the system will be broken if the magnitude of the imaginary part of the external potential exceeds a critical value. Secondly, various of gap solitons were found by the Newton-Conjugate-Gradient method. Finally, the stability properties of gap solitons were investigated through the linear stability analysis and the direct long-time nonlinear dynamical evolution. The results indicated that the stability of on-site and off-site solitons was remarkably influenced by three-body interactions. There exists unstable on-site gap solitons when the PT-symmetric potential is taken into account. Additionally, the magnitude of the imaginary part of the potential also affects the profile and stability of the gap solitons. When it increases, the symmetry of the solitons will be broken.
We report new types of matter rogue waves of a spinor (three-component) model of the Bose-Einstein condensate governed by a system of three nonlinearly coupled Gross-Pitaevskii equations. The exact first-order rational solutions containing one free parameter are obtained by means of a Darboux transformation for the integrable system where the mean-field interaction is attractive and the spin-exchange interaction is ferromagnetic. For different choices of the parameter, there exists a variety of different shaped solutions including two peaks in bright rogue waves and four dips in dark rogue waves. Furthermore, by utilizing the relation between the three-component and the one-component versions of the nonlinear Schrödinger equation, we can devise higher-order rational solutions, in which three components have different shapes. In addition, it is noteworthy that dark rogue wave features disappear in the third-order rational solution.