Nondegenerate bound-state solitons in multicomponent Bose-Einstein condensates

Yan-Hong Qin, Li-Chen Zhao, and Liming Ling

Phys. Rev. E 100, 022212 – Published 15 August 2019

Abstract

We investigate nondegenerate bound-state solitons systematically in multicomponent Bose-Einstein condensates, through developing the Darboux transformation method to derive exact soliton solutions analytically. In particular, we show that bright solitons with nodes correspond to the excited bound states in effective quantum wells, in sharp contrast to the bright solitons and dark solitons reported before (which usually correspond to ground state and free state, respectively). We further demonstrate that bound-state solitons with nodes are induced by incoherent superposition of 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 the same component. Additionally, the detailed spectral stability analysis demonstrates the stability of nondegenerate bound-state solitons. The bound-state solitons can be used to study many different physical problems, such as beating dynamics, spin-orbit coupling effects, quantum fluctuations, and even quantum entanglement states.

Received 15 April 2019
Revised 23 July 2019

DOI:https://doi.org/10.1103/PhysRevE.100.022212

Physics Subject Headings (PhySH)

Bose-Einstein condensates

Collective dynamics Solitons

Atomic, Molecular & OpticalGeneral PhysicsNonlinear Dynamics

Authors & Affiliations

Yan-Hong Qin^1,2, Li-Chen Zhao ^1,2,*, and Liming Ling^3,†

¹School of Physics, Northwest University, Xi'an 710127, China
²Shaanxi Key Laboratory for Theoretical Physics Frontiers, Xi'an 710127, China
³School of Mathematics, South China University of Technology, Guangzhou 510640, China

^*zhaolichen3@nwu.edu.cn
^†linglm@scut.edu.cn

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Issue

Vol. 100, Iss. 2 — August 2019

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Images

Figure 1
Three different density profiles for double-hump solitons in two-component coupled systems: (a1) asymmetric double-hump solitons in both components, (a2) symmetric single-hump–double-hump solitons, and (a3) approximate symmetric double-hump solitons in both components. solid blue line and the dashed red line correspond to the $q_{1}$ component and the $q_{2}$ component, respectively. It is seen that solitons in $q_{1}$ and $q_{2}$ components correspond to first-excited state and ground state, respectively, in the effective double-well potential. The parameters are as follows: (a1) $c_{11} = c_{22} = 1, a_{1} = 0, b_{1} = 1, b_{2} = 1.1$ , and $δ = - 2.8$ ; (a2) $c_{11} = c_{22} = \sqrt{3} / 3, a_{1} = 0, b_{1} = 1, b_{2} = 2 b_{1}$ , and $δ = 0$ ; and (a3) $c_{11} = c_{22} = 1, a_{1} = 0, b_{1} = 2, b_{2} = 2.001$ , and $δ = - 4.1$ .
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Figure 2
The incoherent interactions between solitons in different components with different relative velocities ( $2 a_{1}$ – $2 a_{2}$ ). From top to bottom, the parameters are as follows: (a1) and (a2) $a_{1} = - a_{2} = 0.02$ , (b1) and (b2) $a_{1} = - a_{2} = 0.001$ , and (c1) and (c2) $a_{1} = - a_{2} = 0.0001$ . The left panels show the density distributions of the $q_{1}$ component; the right panels show the density distributions of the $q_{2}$ component. The evolution dynamics suggest that nondegenerate bound-state solitons are induced by incoherent superpositions of bright solitons in different components. The other parameters are $c_{11} = c_{22} = 1, b_{1} = 1, b_{2} = 1.1$ , and $δ = - 2.8$ [the same as those in Fig. 1].
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Figure 3
The collision dynamics between one nondegenerate bound-state soliton and one degenerate bright soliton or one nondegenerate bound-state soliton. (a1) and (a2): The interference behavior between an asymmetric double-hump soliton (moving to the right direction) and a degenerate bright soliton (moving to the left direction). Related parameters are $c_{21} = c_{12} = 0, c_{11} = c_{22} = c_{13} = c_{23} = 1, a_{1} = - 10, a_{2} = 10, b_{1} = 1, b_{2} = 1.1, b_{3} = 0.8$ , and $δ_{1} = δ_{2} = 0$ . (b1) and (b2): The interference patterns between two nondegenerate bound-state solitons. The parameters are $c_{11} = c_{22} = c_{13} = c_{24} = \sqrt{3} / 3, a_{1} = 10, a_{2} = - 10, b_{1} = 1, b_{2} = 2, b_{3} = 1, b_{4} = 2$ , and $δ_{1} = δ_{2} = 0$ . The top panels show the density of the first component, and the bottom panels show the density of the second component. The soliton profiles change too slightly to be visible after the collision at these parameters.
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Figure 4
The inelastic collision between two nondegenerate bound-state solitons. Left panels: Dynamical evolution for coherent collision of nondegenerate bound-state solitons. Right panels: Intensity plots for both components before ( $t = - 30$ , solid blue line) and after ( $t = 30$ , dashed red line) the collision. It is seen that profiles of double-hump solitons indeed change after the collision. The analysis suggests that the collisions between these bound-state solitons are usually inelastic, due to the incoherent interaction and the coherent collision between them. The parameters are $c_{11} = c_{22} = c_{13} = c_{24} = 1, a_{1} = - 1 / 10, a_{2} = 1 / 10, b_{1} = 1, b_{2} = 1.2, b_{3} = 2, b_{4} = 1.9$ , and $δ_{1} = δ_{2} = 0 .$
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Figure 5
Intensity profiles for triple-hump bright solitons of three-component BECs. The triple-hump bright soliton with no node in the $q_{3}$ component is the ground bound state (dashed green line), the triple-hump bright soliton with one node in the $q_{2}$ component is the first-excited bound state (dotted-dashed blue line), and the triple-hump bright soliton with two nodes in the $q_{1}$ component is the second-excited bound state (solid red line) in the effective quantum wells. The parameters are $c_{1} = c_{2} = c_{3} = 1, a_{1} = 0, b_{1} = 1.99, b_{2} = 2, b_{3} = 2.02$ , and $δ = - 5.2$ .
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Figure 6
The excitation spectrum of nondegenerate bound-state solitons. It is seen that nondegenerate bound-state solitons admit spectral stability. The related parameters are same as those in Fig. 1.
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