Bright Soliton Trains of Trapped Bose-Einstein Condensates

Khawaja, U. Al; Stoof, H. T. C.; Hulet, Randall G.; Strecker, Kevin E.; Partridge, Guthrie B.

doi:10.1103/physrevlett.89.200404

Cited by 225 publications

(247 citation statements)

References 26 publications

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“…In this manner, the solitary waves are predicted to be able to survive many collisions without collapse, as were observed in the JILA experiment. This is in general agreement with other work predicting that the multiple soliton-trains seen in experiment [9,11] are consistent with neighbouring solitary waves having a relative phase close to π [22,[38][39][40]72,82]. The origin, and even the true existence, of these π-phase differences is an open question, and will be discussed in Section 7.…”

Section: Stability Of Solitary Wave Collisionssupporting

confidence: 91%

“…In the two experiments to date that have generated multiple bright solitary waves [9,11], the observed wave dynamics (post-formation of the waves) could be well described by the mean-field GPE under the assumption that the waves featured phase differences close to π [38,72,82]. This pattern of relative phases can potentially be explained by a process of solitary wave formation through modulational instability, followed by collapse of neighbouring solitons with relative phases close to zero [22,[38][39][40].…”

Section: Beyond-mean-field Treatments and Relative Phasementioning

confidence: 87%

“…This factorization has often been applied in the study of attractively-interacting condensates (in both dynamic and static situations) [37][38][39][40][41][42]. However, the regime in which this factorization is valid is significantly restricted for attractively-interacting condensates [43]; this issue is revisited using a full 3D analysis in Section 4.…”

Section: Quasi-one-dimensional Gpementioning

confidence: 99%

“…This pattern of relative phases can potentially be explained by a process of solitary wave formation through modulational instability, followed by collapse of neighbouring solitons with relative phases close to zero [22,[38][39][40]. However, the mean-field GPE, even when supplemented with phenomenological three-body loss terms, cannot provide a quantitatively accurate description of solitary wave formation out of a condensate collapse [67,69,92].…”

Section: Beyond-mean-field Treatments and Relative Phasementioning

confidence: 99%

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Spontaneous Symmetry Breaking, Self-Trapping, and Josephson Oscillations

Malomed¹

2013

Progress in Optical Science and Photonics

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In recent years, bright soliton-like structures composed of gaseous Bose-Einstein condensates have been generated at ultracold temperature. The experimental capacity to precisely engineer the nonlinearity and potential landscape experienced by these solitary waves offers an attractive platform for fundamental study of solitonic structures. The presence of three spatial dimensions and trapping implies that these are strictly distinct objects to the true soliton solutions. Working within the zero-temperature mean-field description, we explore the solutions and stability of bright solitary waves, as well as their interactions. Emphasis is placed on elucidating their similarities and differences to the true bright soliton. The rich behaviour introduced in the bright solitary waves includes the collapse instability and symmetry-breaking collisions. We review the experimental formation and observation of bright solitary matter waves to date, and compare to theoretical predictions. Finally we discuss the current state-of-the-art of this area, including beyond-mean-field descriptions, exotic bright solitary waves, and proposals to exploit bright solitary waves in interferometry and as surface probes.

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Section: Stability Of Solitary Wave Collisionssupporting

confidence: 91%

Section: Beyond-mean-field Treatments and Relative Phasementioning

confidence: 87%

Section: Quasi-one-dimensional Gpementioning

confidence: 99%

Section: Beyond-mean-field Treatments and Relative Phasementioning

confidence: 99%

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Spontaneous Symmetry Breaking, Self-Trapping, and Josephson Oscillations

Malomed¹

2013

Progress in Optical Science and Photonics

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“…29) The experimental realization of a BEC bright soliton means that, from Eq. (27), the key parameter A = LV 0 satisfies π/2 < A < 3π/2. We have shown that double pulses with moderate separation develop into a three-soliton state if each pulse satisfies A ∼ 2.25.…”

Section: Discussion and Concluding Remarksmentioning

confidence: 99%

Roles of Interfering Radiation Emitted from Decaying Pulses Obeying Soliton Equations Belonging to the Ablowitz–Kaup–Newell–Segur Systems

Fujishima

Yajima

2015

J. Phys. Soc. Jpn.

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The nonlinear Schrödinger (NLS) equation under the box-type initial condition, which models general multiple pulses deviating from pure solitons, is analyzed. Following the approximation by splitting the initial pulse into many small bins [G. Boffetta and A. R. Osborne, J. Comp. Phys. 102, 25 (1992)], we can analyze the Zakharov-Shabat eigenvalue problem to construct transfer matrices connecting the Jost functions in each interval without direct numerical computation. We can obtain analytical expressions for the scattering data that describe interfering radiation emitted from initial pulses. The number of solitons that appear in the final stage is predicted theoretically, and the condition generating an unusual wave such as a double-pole soliton is derived. Numerical analyses under box-type initial conditions are also performed to show that the interplay between the tails from decaying pulses can affect the asymptotic profile.

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Dissipation-managed soliton in a quasi-one-dimensional Bose-Einstein condensate

Adhikari

2006

Laser Phys. Lett.

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Abstract:We use the time-dependent mean-field GrossPitaevskii equation to study the formation of a dynamicallystabilized dissipation-managed bright soliton in a quasi-onedimensional Bose-Einstein condensate (BEC). Because of threebody recombination of bosonic atoms to molecules, atoms are lost (dissipated) from a BEC. Such dissipation leads to the decay of a BEC soliton. We demonstrate by a perturbation procedure that an alimentation of atoms from an external source to the BEC may compensate for the dissipation loss and lead to a dynamically-stabilized soliton. The result of the analytical perturbation method is in excellent agreement with mean-field numerics. It seems possible to obtain such a dynamically-stabilized BEC soliton without dissipation in laboratory. [5][6][7][8][9], whereas dark solitons represent local minima [2][3][4]. In addition to the observation of an isolated bright soliton in an expulsive potential [6], a number of bright solitons forming a soliton train was observed by Strecker et al. [5], where they suddenly turned a repulsive BEC of 7 Li atoms attractive by manipulating an external magnetic field near a Feshbach resonance [10]. Consequently, the BEC collapsed, exploded and generated a soliton train which was studied in detail. Also, a bright vector soliton in a repulsive BEC supported by interspecies attraction has been studied [11,12].A soliton or solitary wave by definition propagates over large time intervals without visible modification of shape which makes it of special interest. However, a soliton of BEC, or a BEC in general, suffer loss of atoms due to three-body recombination leading to formation of molecules [13][14][15]. This means that a BEC soliton will decay and eventually disappear as it propagates. It would be of interest if an artificial situation could be created in laboratory with a supply of atoms so as to compensate for the three-body recombination loss of a BEC soliton to generate a dynamically-stabilized soliton. To the best of our knowledge we demonstrate for the first time, using the mean-field Gross-Pitaevskii (GP) equation [16], that such a dynamically stabilized soliton could indeed be prepared in a radially trapped and axially free BEC. As a strict soliton appears only in one dimension, we shall be concerned in this paper with a quasi-one-dimensional BEC soliton in a cigar-shaped trap in a axially symmetric configuration.To demonstrate the presence of a dynamicallystabilized dissipation-managed BEC soliton, we employ both time-dependent and time-independent analytic perturbation techniques and a complete numerical solution of the GP equation. The numerical result is found to be in ex-

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Bright Soliton Trains of Trapped Bose-Einstein Condensates

Cited by 225 publications

References 26 publications

Spontaneous Symmetry Breaking, Self-Trapping, and Josephson Oscillations

Spontaneous Symmetry Breaking, Self-Trapping, and Josephson Oscillations

Roles of Interfering Radiation Emitted from Decaying Pulses Obeying Soliton Equations Belonging to the Ablowitz–Kaup–Newell–Segur Systems

Dissipation-managed soliton in a quasi-one-dimensional Bose-Einstein condensate

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