Dark-bright solitons and their lattices in atomic Bose-Einstein condensates

Yan, Dong; Tsitoura, F.; Kevrekidis, P. G.; Frantzeskakis, D. J.

doi:10.1103/physreva.91.023619

Cited by 27 publications

(42 citation statements)

References 34 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…We therefore checked the dynamical stability of the stationary dark-bright soliton state. In accordance with the results of [38], we found there is some instability but nevertheless the corresponding growth rate is rather small, i.e., small enough that over the time scales reported herein, the resulting weak dynamical instabilities (of stationary states) have not yet set in. Our detailed examination of this feature suggests that during the intermediate, as well as disordered phase dynamics, the collisional dynamics may develop high amplitudes, thus rendering some of the bright solitons less visible in the space-time plots of e.g.…”

Section: B Dark-bright Solitonssupporting

confidence: 92%

“…A few examples of both in-phase and outof-phase DBS stationary states are shown in Figure 2 and 3 respectively. The few DBS states are in line with the states reported in [28], while a discussion of DBS consisting of many waves and possible analytical DBS-lattice solutions based on elliptic functions are given in [38].…”

Section: B Identification and Continuation Of Stationary Dbs Statessupporting

confidence: 59%

“…for a recent example of a relevant discussion [37]), and dark-bright solitons (see e.g. for a recent example [38]). For these arrays, we intend to describe "transitions" between ordered, crystalline-type states to disordered, gaseous-type states.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Transitions from order to disorder in multiple dark and multiple dark-bright soliton atomic clouds

Wang

Kevrekidis

2015

Phys. Rev. E

Self Cite

View full text Add to dashboard Cite

We have performed a systematic study quantifying the variation of solitary wave behavior from that of an ordered cloud resembling a "crystalline" configuration to that of a disordered state that can be characterized as a soliton "gas". As our illustrative examples, we use both one-component, as well as two-component, one dimensional atomic gases very close to zero temperature, where in the presence of repulsive inter-atomic interactions and of a parabolic trap, a cloud, respectively of dark (dark-bright) solitons can form in the one-(two-) component system. We corroborate our findings through three distinct types of approaches, namely a Gross-Pitaevskii type of partial differential equation, particle-based ordinary differential equations describing the soliton dynamical system and Monte-Carlo simulations for the particle system. We define an "empirical" order parameter to characterize the order of the soliton lattices and study how this changes as a function of the strength of the "thermally" (i.e., kinetically) induced perturbations. As may be anticipated by the one-dimensional nature of our system, the transition from order to disorder is gradual without, apparently, a genuine phase transition ensuing in the intermediate regime.

show abstract

Section: B Dark-bright Solitonssupporting

confidence: 92%

Section: B Identification and Continuation Of Stationary Dbs Statessupporting

confidence: 59%

See 1 more Smart Citation

Transitions from order to disorder in multiple dark and multiple dark-bright soliton atomic clouds

Wang

Kevrekidis

2015

Phys. Rev. E

Self Cite

View full text Add to dashboard Cite

show abstract

“…In the 1D case studied in Ref. [48], it has been observed that the stability of the individual dark-bright solitons is not dramatically affected by the variation of σ 12 . Similar findings are observed in the present 2D case, although the instability growth rates start decreasing, resulting in a small stability region close to the upper bound of the examined window of σ 12 (see the bottom panel of Fig.…”

Section: B Numerical Resultsmentioning

confidence: 96%

Vortex-soliton complexes in coupled nonlinear Schrödinger equations with unequal dispersion coefficients

et al. 2016

Self Cite

View full text Add to dashboard Cite

We consider a two-component, two-dimensional nonlinear Schrödinger system with unequal dispersion coefficients and self-defocusing nonlinearities, chiefly with equal strengths of the self-and cross-interactions. In this setting, a natural waveform with a nonvanishing background in one component is a vortex, which induces an effective potential well in the second component, via the nonlinear coupling of the two components. We show that the potential well may support not only the fundamental bound state, but also multi-ring excited radial state complexes for suitable ranges of values of the dispersion coefficient of the second component. We systematically explore the existence, stability, and nonlinear dynamics of these states. The complexes involving the excited radial states are weakly unstable, with a growth rate depending on the dispersion of the second component. Their evolution leads to transformation of the multi-ring complexes into stable VB solitons ones with the fundamental state in the second component. The excited states may be stabilized by a harmonic-oscillator trapping potential, as well as by unequal strengths of the self-and cross-repulsive nonlinearities.

show abstract

“…The dark-bright soliton solutions to the Manakov model are given by [204] , , where E B = a 2 /2 is the 'binding energy' of the bright component [204] . If the coupling strengths are tuned away from the integrable point, it is sometimes possible to find closed form dark bright solitary wave solutions [204,242,244,245] . However, in most parameter regimes solutions must be found numerically [191] .…”

Section: Methodsmentioning

confidence: 99%

Non-equilibrium dynamics of Bose Einstein condensates

Mills¹

View full text Add to dashboard Cite

This thesis examines two aspects of the non-equilibrium dynamics of Bose-Einstein condensates (BECs). Our particular interests are the relaxation of near-integrable systems, and the inter-particle correlations present in BECs, both in equilibrium and following an abrupt change in the Hamiltonian.In the first part of this thesis we investigate the stability of solitary wave solutions to a system of two coupled one-dimensional non-linear Schrödinger equations (CNLSE). This system has an integrable point known as the Manakov [1] model which has analytic dark-bright soliton solutions [2] . We break the integrability of this model by varying the inter-species interaction strength, and employ variational and numerical methods in order to find dark-bright solitary wave solutions, away from the integrable point.The time evolution of these states is calculated via numerical integration of the CNLSE, which allows us to assess the stability of these solutions in isolation and to quantify their robustness against collisions with a dark soliton. We find that there is a broad region of the parameter space in which solutions for black-bright (stationary) solitary waves can be found. In this domain, the integrability breaking is revealed only during collisions. Prior to a collision, the numerical solutions are indistinguishable from true solitons, however, the collisional stability of these solitary waves is significantly affected by the extent to which integrability is broken. We find that there is a smooth transition between the non-dispersive particle-like nature of soliton interactions for integrable systems, and the destructive collisions which take place when the system is perturbed far from the integrable point.In the case of moving (grey-bright) solitary waves, we find a more restricted region of the parameter space which admits solitary wave solutions. In this domain we are able to find approximately stable solitary wave solutions using a variational ansatz. The collisional stability of these grey-bright solitary waves is also found to depend upon the extent to which integrability is broken.We conclude that the observation of stable, long-lived dark-bright solitary waves is not sufficient to indicate near-integrability of the two-component system. However, near-integrability may inferred if dark-bright solitary waves are observed to survive multiple collisions. These results are not only of theoretical interest, but may also inform future experiments which explore the behaviour of solitary waves in two-component Bose-Einstein condensates.Following this we investigate the properties of magnetic solitary wave solutions to the CNLSE. We find that the analytic 'magnetic soliton' solutions derived in reference [3] are dynamically unstable and relax to non-stationary magnetic solitary wave states over a short timescale. We investigate the collisional dynamics of these magnetic solitary waves and find that these excitations are remarkably robust.In the second part of this thesis we calculate the fluctuations in the nu...

show abstract

Dark-bright solitons and their lattices in atomic Bose-Einstein condensates

Cited by 27 publications

References 34 publications

Transitions from order to disorder in multiple dark and multiple dark-bright soliton atomic clouds

Transitions from order to disorder in multiple dark and multiple dark-bright soliton atomic clouds

Vortex-soliton complexes in coupled nonlinear Schrödinger equations with unequal dispersion coefficients

Non-equilibrium dynamics of Bose Einstein condensates

Contact Info

Product

Resources

About