Non-integrable dynamics of matter-wave solitons in a density-dependent gauge theory

Dingwall, Robert James; Edmonds, Matthew; Helm, John L.; Malomed, Boris A.; Öhberg, Patrik

doi:10.1088/1367-2630/aab29e

Cited by 32 publications

(32 citation statements)

References 67 publications

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“…The trajectory of the soliton is then set by Eq. (62), which in a consistent manner to Eq. (10), contains an additional contribution from the gauge field.…”

Section: B Variational Equationssupporting

confidence: 79%

Stability of matter-wave solitons in a density-dependent gauge theory

Dingwall

Öhberg

2019

Phys. Rev. A

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We consider the linear stability of chiral matter-wave solitons described by a density-dependent gauge theory. By studying the associated Bogoliubov-de Gennes equations both numerically and analytically, we find that the stability problem effectively reduces to that of the standard Gross-Pitaevskii equation, proving that the solitons are stable to linear perturbations. In addition, we formulate the stability problem in the framework of the Vakhitov-Kolokolov criterion and provide supplementary numerical simulations which illustrate the absence of instabilities when the soliton is initially perturbed.

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“…The trajectory of the soliton is then set by Eq. (62), which in a consistent manner to Eq. (10), contains an additional contribution from the gauge field.…”

Section: B Variational Equationssupporting

confidence: 79%

Stability of matter-wave solitons in a density-dependent gauge theory

Dingwall

Öhberg

2019

Phys. Rev. A

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“…A useful measure for soliton collisions with non-integrable dynamics is the coefficient of restitution. This is a dimensionless quantity defined as the total kinetic energy of two particles after a collision to the total kinetic energy before the collision [65,66]…”

Section: Binary Soliton-impurity Dynamicsmentioning

confidence: 99%

Coherent impurity transport in an attractive binary Bose–Einstein condensate

2019

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We study the dynamics of a soliton-impurity system modeled in terms of a binary Bose-Einstein condensate. This is achieved by 'switching off' one of the two self-interaction scattering lengths, giving a two component system where the second component is trapped entirely by the presence of the first component. It is shown that this system possesses rich dynamics, including the identification of unusual 'weak' dimers that appear close to the zero inter-component scattering length. It is further found that this system supports quasi-stable trimers in regimes where the equivalent single-component gas does not, which is attributed to the presence of the impurity atoms which can dynamically tunnel between the solitons, and maintain the required phase differences that support the trimer state. that the single component focussing nonlinear Schrödinger equation can possess chaotic solutions in the presence of an axial harmonic potential [29,30], as well as the observed interaction induced frequency shift of pairs of trapped bright solitons [31] in the experiment of [13]. Complementary to this, theoretical work has focussed on solitary waves in higher spin systems, revealing the existance of integrable points in the full parameter space of the spin-1 condensate, in the form of so-called 'polar' bright solitons [32,33]. Although solitons are usually studied as the solutions to one-dimensional nonlinear models, there have also been predictions of stable two-dimensional solitary wave solutions in dipolar Bose-Einstein condensates [34,35], where the additional nonlocal nonlinearity provides the stabilizing mechanism for these solitons. Very recently the Jones-Roberts soliton was realized experimentally, a true two-dimensional solitary wave structure [36].The realization of artificial electromagnetism with cold gases, and in particular spin-orbit coupling for Bose-Einstein condensates opens a novel route towards studying nonlinear wave structures. Here, the coupling of the condensates momentum to a quasi-spin leads to stripe-like soliton phases, related to the underlying immiscible phase of these systems [37,38]. Spin-orbit coupling forms a key ingredient in simulating more exotic scenarios, such as Dirac-like equations, where confined solutions have been predicted [39] that resemble their bright soliton cousins in single component condensates.Atomic condensates benefit from being exceptionally pure systems-this in turn allows one to investigate the effects of disorder and defects with an unprecedented level of control. The presence of impurities in ensembles of ultracold matter has led to predictions of impurity-molecules and lattices at the mean-field level [40], as well as the role of many-body correlations for a single impurity out-of-equilibrium [41]. Experimental work has studied the role that spin impurities have in the strongly correlated Tonks-Girardeau limit [42] and also magnetic spin models [43], which have also been the focus of subsequent theoretical investigations [44][45][46]. Complementary to this, recent exper...

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“…Indeed, let us consider the projection of the original system of the equations onto the lowest energy spin state in adiabatic approximation [54]. Diagonalizing the Hamiltonian associated with system (1) in the basis of dressed states, one observes that in the limit of small densities |ψ ± | 1 the adiabatic dynamics is governed by the following effective density-dependent Hamiltonian [55]: H = (p − A) 2 + g|ψ 1 | 2 , wherep = −i∂ ϕ is the momentum operator, |ψ 1 | 2 is the local squared density of ψ +component in one of the dressed states, g is the effective nonlinearity coefficient [56]:…”

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confidence: 99%

Chiral solitons in spinor polariton rings

et al. 2018

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We consider theoretically one-dimensional polariton ring accounting for both longitudinal-transverse (TE-TM) and Zeeman splitting of spinor polariton states and spin dependent polaritonpolariton interactions. We present the novel class of solutions in the form of the localized defects rotating with constant angular velocity and analyze their properties for realistic values of the parameters of the system. We show that the effects of the geometric phase arising from the interplay between external magnetic field and TE-TM splitting introduce chirality in the system and make solitons propagating in clockwise and anticlockwise directions non equivalent. This can be interpreted as solitonic analog of Aharonov-Bohm effect. arXiv:1711.02872v3 [cond-mat.mes-hall]

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Non-integrable dynamics of matter-wave solitons in a density-dependent gauge theory

Cited by 32 publications

References 67 publications

Stability of matter-wave solitons in a density-dependent gauge theory

Stability of matter-wave solitons in a density-dependent gauge theory

Coherent impurity transport in an attractive binary Bose–Einstein condensate

Chiral solitons in spinor polariton rings

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