Dynamics of a Bright Soliton in Bose-Einstein Condensates with Time-Dependent Atomic Scattering Length in an Expulsive Parabolic Potential

Liang, Zhaoxin; Zhang, Z. D.; Liu, W. M.

doi:10.1103/physrevlett.94.050402

Cited by 404 publications

(269 citation statements)

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“…Static and dynamical properties of Bose-Einstein condensates have been extensively and successfully explored in the community by employing the mean-field Gross-Pitaevskii theory [11,12], for reviews see [8][9][10] and for individual applications to condensates and mixtures [13][14][15][16][17][18][19] and [20][21][22][23][24][25], respectively. Gross-Pitaevskii theory is an excellent theory for weaklyinteracting bosons whenever a single macroscopic one-particle wavefunction is sufficient to describe the reality.…”

Section: Introductionmentioning

confidence: 99%

Multiconfigurational time-dependent Hartree method for bosons: Many-body dynamics of bosonic systems

2008

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The evolution of Bose-Einstein condensates is amply described by the time-dependent GrossPitaevskii mean-field theory which assumes all bosons to reside in a single time-dependent oneparticle state throughout the propagation process. In this work, we go beyond mean-field and develop an essentially-exact many-body theory for the propagation of the time-dependent Schrödinger equation of N interacting identical bosons. In our theory, the time-dependent many-boson wavefunction is written as a sum of permanents assembled from orthogonal one-particle functions, or orbitals, where both the expansion coefficients and the permanents (orbitals) themselves are timedependent and fully determined according to a standard time-dependent variational principle. By employing either the usual Lagrangian formulation or the Dirac-Frenkel variational principle we arrive at two sets of coupled equations-of-motion, one for the orbitals and one for the expansion coefficients. The first set comprises of first-order differential equations in time and non-linear integro-differential equations in position space, whereas the second set consists of first-order differential equations with time-dependent coefficients. We call our theory multi-configurational timedependent Hartree for bosons, or MCTDHB(M ), where M specifies the number of time-dependent orbitals used to construct the permanents. Numerical implementation of the theory is reported and illustrative numerical examples of many-body dynamics of trapped Bose-Einstein condensates are provided and discussed.

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Section: Introductionmentioning

confidence: 99%

Multiconfigurational time-dependent Hartree method for bosons: Many-body dynamics of bosonic systems

2008

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“…[15], numerous studies of the one-dimensional NLS equation with combined temporal modulation of various coefficients, including also linear dissipation, have recently been reported [16,17], where the main attention was focused on properties of solitary wave solutions.…”

Section: Introductionmentioning

confidence: 99%

Similarity transformations for nonlinear Schrödinger equations with time-dependent coefficients

Pérez-Garcı́a

Torres

Konotop

2006

Physica D: Nonlinear Phenomena

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In this paper we use a similarity transformation connecting some families of Nonlinear Schrödinger equations with time-varying coefficients with the autonomous cubic nonlinear Schrödinger equation. This transformation allows one to apply all known results for that equation to the original non-autonomous case with the additional dynamics introduced by the transformation itself. In particular, using stationary solutions of the autonomous nonlinear Schrödinger equation we can construct exact breathing solutions to multidimensional non-autonomous nonlinear Schrödinger equations. An application is given in which we explicitly construct time dependent coefficients leading to solutions displaying weak collapse in three-dimensional scenarios. Our results can find physical applicability in mean field models of Bose-Einstein condensates and in the field of dispersion-managed optical systems.

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“…Lm, 05.45.Yv, Coherent atom optics is the subject of much current interest due to its relevance to both fundamental aspects of physics, as well as to technology [1,2,3,4,5,6]. For that purpose, lower dimensional condensates e.g., cigarshaped Bose-Einstein condensates (BECs) have been the subject of active study in the last few years [7,8,9,10,11]. Observations of dark and bright solitons [12,13,14], particularly the latter one, since the same is a condensate itself, have generated considerable interest in this area.…”

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confidence: 99%

Class of solitary wave solutions of the one-dimensional Gross-Pitaevskii equation

2006

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We present a large family of exact solitary wave solutions of the one dimensional GrossPitaevskii equation, with time-varying scattering length and gain/loss, in both expulsive and regular parabolic confinement regimes. The consistency condition governing the soliton profiles is shown to map on to a linear Schrödinger eigenvalue problem, thereby enabling one to find analytically the effect of a wide variety of temporal variations in the control parameters, which are experimentally realizable. Corresponding to each solvable quantum mechanical system, one can identify a soliton configuration. These include soliton trains in close analogy to experimental observations of Strecker et al., [Nature 417, 150 (2002)], spatio-temporal dynamics, solitons undergoing rapid amplification, collapse and revival of condensates and analytical expression of two-soliton bound states, to name a few.PACS numbers: 03.75. Lm, 05.45.Yv, Coherent atom optics is the subject of much current interest due to its relevance to both fundamental aspects of physics, as well as to technology [1,2,3,4,5,6]. For that purpose, lower dimensional condensates e.g., cigarshaped Bose-Einstein condensates (BECs) have been the subject of active study in the last few years [7,8,9,10,11]. Observations of dark and bright solitons [12,13,14], particularly the latter one, since the same is a condensate itself, have generated considerable interest in this area. This has spurred intense investigations about the behavior of condensates in the presence of time-varying control parameters. These include nonlinearity, achievable through Feshbach resonance [15,16,17], gain/loss and the oscillator frequency [18]. The fact that for a condensate in oscillator potential, exact solutions of the Gross-Pitaevskii (GP) equation are not available, makes it extremely difficult to examine the effects of time variation in the aforementioned parameters. In the context of pulse propagation in non-linear optical fibers, a number of authors have recently investigated the effects of variable non-linearity, dispersion and gain or loss. Moores analyzed this problem for constant dispersion and nonlinearity and a distributed gain [19] and obtain a number of exact solutions. Recently, exact solutions of a driven NLSE with distributed dispersion, nonlinearity and gain, which exhibits pulse compression in a twin-core optical fiber, has also been obtained [22].In this Letter, we present a large family of exact solutions of the quasi one-dimensional GP equation, which is the familiar NLSE, with time varying scattering length, gain/loss, in the presence of an oscillator potential, which can be both expulsive or regular. It is shown that, the consistency condition governing the soliton profiles identically maps on to the linear Schrödinger eigenvalue problem, thereby allowing one to solve analytically the GP equation for a wide variety of temporal variations in the control parameters. Corresponding to each solvable quantum mechanical eigenvalue problem, one can identify a soliton-like profile. The...

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Dynamics of a Bright Soliton in Bose-Einstein Condensates with Time-Dependent Atomic Scattering Length in an Expulsive Parabolic Potential

Cited by 404 publications

References 32 publications

Multiconfigurational time-dependent Hartree method for bosons: Many-body dynamics of bosonic systems

Multiconfigurational time-dependent Hartree method for bosons: Many-body dynamics of bosonic systems

Similarity transformations for nonlinear Schrödinger equations with time-dependent coefficients

Class of solitary wave solutions of the one-dimensional Gross-Pitaevskii equation

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