Scattering of solitons in binary Bose–Einstein condensates with spin-orbit and Rabi couplings

Cardoso, Wesley B.; Teixeira, Rafael M. P.

doi:10.1007/s11071-019-04846-5

“…The red line in Fig. 4 (b1) shows the profile of RW structure |ψ| when t = 1 4 ln 3 2 in solution (13). According to the above analysis, the RW solution has a localized peak value of around 7.35 at the point |ψ|max and a localized depression value of 0 at two points |ψ| min,± .…”

Section: Discussionmentioning

confidence: 77%

“…Localized waves and mixed interaction solutions with dynamical analysis to the Gross-Pitaevskii equation in the Bose-Einstein condensate 1…”

mentioning

confidence: 99%

See 1 more Smart Citation

Localized waves and mixed interaction solutions with dynamical analysis to the Gross-Pitaevskii equation in the Bose-Einstein condensate

Wang

¹

,

Zhou

²

,

Biswas

³

et al. 2021

Preprint

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We report a kind of breather, rogue wave and mixed interaction structures on a variational background height in the Gross-Pitaevskii equation in the Bose-Einstein condensate by the generalized Darboux transformation method, and the effects of related parameters on rogue wave structures are discussed. Numerical simulation can discuss the dynamics and stability of these solutions. We numerically confirm that these are correct, and can be reproduced from a deterministic initial profile. Results show that rogue waves and mixed interaction solutions can evolve with a small amplitude perturbation under the initial profile conditions, but breathers cannot. Therefore, these can be used to anticipate the feasibility of their experimental observation.

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“…Refs. [31,[36][37][38]), and the contact self-interaction in each component (if any) is represented by coefficient g (g > 0 and g < 0 correspond to self-attraction and repulsion, respectively). Contact cross-interaction between the components can be readily added to the system, in the form of terms ∼ |φ ∓ | 2 φ ± in each equation, but they do not produce essential changes in the results reported below.…”

Section: The Modelmentioning

confidence: 99%

Gap and embedded solitons in microwave-coupled binary condensates

Fan

¹

,

Chen

²

,

Li

³

et al. 2020

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It was recently found that, under the action of the spin-orbit coupling (SOC) and Zeeman splitting (ZS), binary BEC with intrinsic cubic nonlinearity supports families of gap solitons, provided that the kinetic energy is negligible in comparison with the SOC and ZS terms. We demonstrate that, also under the action of SOC and ZS, a similar setting may be introduced for BEC with two components representing different atomic states, resonantly coupled by microwave radiation, while the Poisson's equation accounts for the feedback of the two-component atomic wave function onto the radiation. The microwave-mediated interaction induces an effective nonlinear trapping potential, which strongly affects the purport of the linear spectrum in this system. As a result, families of both gap and embedded solitons (those overlapping with the continuous spectrum) are found, which are chiefly stable. The shape of the solitons features exact or broken skew symmetry. In addition to fundamental solitons (whose shape may or may not include a node), a family of dipole solitons is constructed too, which are even more stable than their fundamental counterparts. A nontrivial stability area is identified for moving solitons in the present system, which lacks Galilean invariance. Colliding solitons merge into a single one.

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“…As a new state of matter and a field in physics, the surge of interest in Bose-Einstein condensate (BEC) has been prompted in recent years by researchers [1][2][3][4][5][6][7]. The mean-field Gross-Pitaevskii equation (GPE) is used to describe and understand some nonlinear phenomena, interesting and important properties and characteristics of vortex states [8][9][10][11][12] and localized waves including soliton [13][14][15][16], rogue wave (RW) [17][18][19], breather [20,21] in BEC, which is also one of the main theoretical research methods, and some predictions have been exposed to agree with relevant vortex and localized wave experiments [22][23][24].…”

Section: Introductionmentioning

confidence: 99%

Localized waves and mixed interaction solutions with dynamical analysis to the Gross–Pitaevskii equation in the Bose–Einstein condensate

Wang

¹

,

Zhou

²

,

Biswas

³

et al. 2021

View full text Add to dashboard Cite

We report a kind of breather, rogue wave and mixed interaction structures on a variational background height in the Gross-Pitaevskii equation in the Bose-Einstein condensate by the generalized Darboux transformation method, and the effects of related parameters on rogue wave structures are discussed. Numerical simulation can discuss the dynamics and stability of these solutions. We numerically confirm that these are correct, and can be reproduced from a deterministic initial profile. Results show that rogue waves and mixed interaction solutions can evolve with a small amplitude perturbation under the initial profile conditions, but breathers cannot. Therefore, these can be used to anticipate the feasibility of their experimental observation.

show abstract

Scattering of solitons in binary Bose–Einstein condensates with spin-orbit and Rabi couplings

Cited by 14 publications

References 93 publications

Localized waves and mixed interaction solutions with dynamical analysis to the Gross-Pitaevskii equation in the Bose-Einstein condensate

Localized waves and mixed interaction solutions with dynamical analysis to the Gross-Pitaevskii equation in the Bose-Einstein condensate

Gap and embedded solitons in microwave-coupled binary condensates

Localized waves and mixed interaction solutions with dynamical analysis to the Gross–Pitaevskii equation in the Bose–Einstein condensate

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