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Chinese Physics B

Soliton breathers in spin-1 Bose—Einstein condensates

Shen-Tong Ji, Pei-Gen Yan, Xue‐Shen Liu

Published Mar 1, 2014• 3 citations
Publisher

Abstract

We consider a spin-1 Bose—Einstein condensate trapped in a harmonic potential with different nonlinearity coefficients. We illustrate the dynamics of soliton breathers in two-component and three-component states by numerically solving the one-dimensional time-dependent coupled Gross—Pitaecskii equations (GPEs). We present that two condensates with repulsive interspecies interactions make elastic collision and novel soliton breathers are created in two-component state. We also demonstrate novel soliton breathers in three-component state with attractive coupling constants. Furthermore, possible reasons for creating soliton breathers are discussed.

DOI
10.1088/1674-1056/23/3/030311

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We consider a spin-1 Bose—Einstein condensate trapped in a harmonic potential with different nonlinearity coefficients. We illustrate the dynamics of soliton breathers in two-component and three-component states by numerically solving the one-dimensional time-dependent coupled Gross—Pitaecskii equations (GPEs). We present that two condensates with repulsive interspecies interactions make elastic collision and novel soliton breathers are created in two-component state. We also demonstrate novel soliton breathers in three-component state with attractive coupling constants. Furthermore, possible reasons for creating soliton breathers are discussed.
The three-coupled Gross-Pitaevskii equation with a harmonic potential in a (2+1)-dimensional spin-1 Bose-Einstein condensate is studied in this paper.Using the Hirota bilinear method, the bright and dark soliton solutions of the system with attractive and repulsive interactions are obtained, and the amplitudes and velocities of those solitons are also given.In addition, we analyze the influence of harmonic potential on the dynamics of solitons and discuss the interaction between solitons through asymptotic analysis.As a result, we find that the amplitude and velocity of solitons are related to the harmonic potential, and the interaction between the two solitons is elastic.
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The dynamics of static and traveling breathers in two-species Bose-Einstein condensates in a one-dimensional optical lattice is modelled within the tight-binding approximation. Two coupled discrete nonlinear Schrödinger equations describe the interaction of the condensates in two cases of relevance: a mixture of two ytterbium isotopes and a mixture of (87)Rb and (41)K. Depending on their initial separation, interaction between static breathers of different species can lead to the formation of symbiotic structures and transform one of the breathers from a static into a traveling one. Collisions between traveling and static discrete breathers composed of different species are separated into four distinct regimes ranging from totally elastic when the interspecies interaction is highly attractive to mutual destruction when the interaction is sufficiently large and repulsive. We provide an explanation of the collision features in terms of the interspecies coupling and the negative effective mass of the discrete breathers.
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.
By numerical and variational analysis of the three-dimensional Gross–Pitaevskii equation, we study the formation and dynamics of bright and vortex-bright solitons in a cigar-shaped dipolar Bose–Einstein condensate for large repulsive atomic interactions. A phase diagram showing the region of stability of the solitons is obtained. We also study the dynamics of breathing oscillation of the solitons as well as the collision dynamics of two solitons. At large velocities the frontal collision is elastic and the two three-dimensional solitons pass through each other undeformed. Two solitons placed side by side at rest coalesce to form a stable bound soliton molecule due to dipolar attraction. Movie clips illustrating collision and molecule-formation dynamics of two bright and vortex-bright solitons are included.
Solitons are non-dispersive wave packets that balance the wave dispersion with a focusing nonlinearity. They maintain their shape and velocity after collisions with other solitons, owing to the integrability of the underlying nonlinear partial differential equations. They appear in various physical systems, such as water waves, light waves in optical fiber, and matter waves. In our laboratory, we study solitons and their interactions in a Bose-Einstein condensate with an attractive nonlinearity, trapped in a quasi-one-dimensional waveguide. We investigate the collisions of a pair of solitons and explore the relative phase implications on the boundary of integrability. We study soliton train formation with the quench of the nonlinearity strength, and interactions between neighboring solitons in the train. We form a composite soliton, known as a breather, where multiple solitons overlap and the wavefunction ``breathes'' in time. We also explore the response of an elongated condensate to an external modulation of the nonlinearity. These experiments characterize the mean-field descriptions of solitons and Bose-Einstein condensates and explore the boundaries between the mean-field theory and quantum many-body theory.