Properties of the temporal–spatial interference pattern during soliton interaction

Zhao, Li-Chen; Ling, Liming; Yang, Zhan-Ying; Liu, Jie

doi:10.1007/s11071-015-2354-0

Cited by 32 publications

(30 citation statements)

References 61 publications

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“…When the soliton velocities are close to the maximum speed, the collision between spin solitons becomes classically elastic. The behavior is similar with the ones in integrable systems [17,18,55]. We show one case with v 1 = −v 2 = 0.9 and ∆φ = 0 (the maximum speed is √ g = 1) in Fig.…”

Section: Collisions Between Spin Solitonssupporting

confidence: 74%

Spin Solitons in Spin-1 Bose-Einstein Condensates

Meng¹,

Qin²,

Zhao³

2019

Preprint

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Solitons in multi-component Bose-Einstein condensates have been paid much attention, due to the stability and wide applications of them. The exact soliton solutions are usually obtained for integrable models. In this paper, we present four families of exact spin soliton solutions for nonintegrable cases in spin-1 Bose-Einstein Condensates. The whole particle density is uniform for the spin solitons, which is in sharp contrast to the previously reported solitons of integrable models. The spectrum stability analysis and numerical simulation indicate the spin solitons can exist stably. The spin density redistribution happens during the collision process, which depends on the relative phase and relative velocity between spin solitons. The non-integrable properties of the systems can bring spin solitons experience weak amplitude and location oscillations after collision. These stable spin soliton excitations could be used to study the negative inertial mass of solitons, the dynamics of soliton-impurity systems, and the spin dynamics in Bose-Einstein condensates.

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Section: Collisions Between Spin Solitonssupporting

confidence: 74%

Spin Solitons in Spin-1 Bose-Einstein Condensates

Meng¹,

Qin²,

Zhao³

2019

Preprint

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“…), in sharp contrast to interference pattern between bright solitons reported before [32]. This comes from the energy eigenvalues are more than two involving the interference process.…”

Section: Collision Between Different Non-degenerated Solitonsmentioning

confidence: 62%

Nondegenerate bound-state solitons in multicomponent Bose-Einstein condensates

2019

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We investigate non-degenerate bound state solitons systematically in multi-component Bose-Einstein condensates, through developing Darboux transformation method to derive exact soliton solutions analytically. In particular, we show that bright solitons with nodes correspond to the excited bound eigen-states in the self-induced effective quantum wells, in sharp contrast to the bright soliton and dark soliton reported before (which usually correspond to ground state and free eigenstate respectively). We further demonstrate that the bound state solitons with nodes are induced by incoherent interactions between solitons in different components. Moreover, we reveal that the interactions between these bound state solitons are usually inelastic, caused by the incoherent interactions between solitons in different components and the coherent interactions between solitons in same component. The bound state solitons can be used to discuss many different physical problems, such as beating dynamics, spin-orbital coupling effects, quantum fluctuations, and even quantum entanglement states.

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“…We emphasize that the analytical solution describing interactions between these soltions can not be derived from the eigen-states in quantum wells. But these solitons with different moving ve-locities can be chosen as initial states to simulate soliton interaction numerically, since when solitons are well separated, they can be seen as the linear superposition of solitons with different velocities approximately [41,42]. For examples, the collision between solitons with nodes were investigated in [43], which demonstrated they were robust to collisions and even noises.…”

Section: Conclusion and Discussionmentioning

confidence: 99%

Solitons in nonlinear systems and eigen-states in quantum wells

Zhao

Yang

2019

Chinese Phys. B

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We study the relations between solitons of nonlinear Schrödinger equation described systems and eigen-states of linear Schrödinger equation with some quantum wells. Many different nondegenerated solitons are re-derived from the eigen-states in the quantum wells. We show that the vector solitons for coupled system with attractive interactions correspond to the identical eigenstates with the ones of coupled systems with repulsive interactions. The energy eigenvalues of them seem to be different, but they can be reduced to identical ones in the same quantum wells. The non-degenerated solitons for multi-component systems can be used to construct much abundant degenerated solitons in more components coupled cases. On the other hand, we demonstrate soliton solutions in nonlinear systems can be also used to solve the eigen-problems of quantum wells. As an example, we present eigenvalue and eigen-state in a complicated quantum well for which the Hamiltonian belongs to the non-Hermitian Hamiltonian having Parity-Time symmetry. We further present the ground state and the first exited state in an asymmetric quantum double-well from asymmetric solitons. Based on these results, we expect that many nonlinear physical systems can be used to observe the quantum states evolution of quantum wells, such as water wave tank, nonlinear fiber, Bose-Einstein condensate, and even plasma, although some of them are classical physical systems. These relations provide another different way to understand the stability of solitons in nonlinear Schrödinger equation described systems, in contrast to the balance between dispersion and nonlinearity.

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Properties of the temporal–spatial interference pattern during soliton interaction

Cited by 32 publications

References 61 publications

Spin Solitons in Spin-1 Bose-Einstein Condensates

Spin Solitons in Spin-1 Bose-Einstein Condensates

Nondegenerate bound-state solitons in multicomponent Bose-Einstein condensates

Solitons in nonlinear systems and eigen-states in quantum wells

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