Dynamics of a matter-wave bright soliton in an expulsive potential

Carr, Lincoln D.

doi:10.1103/physreva.66.063602

Cited by 146 publications

(259 citation statements)

References 32 publications

Supporting

Mentioning

250

Contrasting

Order By: Relevance

“…Both the mean-field approximation, as well as a diagonalization scheme are used to attack the problem. [4,5] have examined theoretically these systems. In the limit where transversely to the long axis of the trap the gas is in the lowest harmonicoscillator level, the transverse degrees of freedom are frozen out and the system is essentially one-dimensional [6].…”

mentioning

confidence: 99%

Bose-Einstein condensates with attractive interactions on a ring

Kavoulakis¹

2003

Phys. Rev. A

View full text Add to dashboard Cite

Considering an effectively attractive quasi-one-dimensional Bose-Einstein condensate of atoms confined in a toroidal trap, we find that the system undergoes a phase transition from a uniform to a localized state, as the magnitude of the coupling constant increases. Both the mean-field approximation, as well as a diagonalization scheme are used to attack the problem. [4,5] have examined theoretically these systems. In the limit where transversely to the long axis of the trap the gas is in the lowest harmonicoscillator level, the transverse degrees of freedom are frozen out and the system is essentially one-dimensional [6].Motivated by these developments, we study here an effectively attractive one-dimensional Bose-Einstein condensate of atoms confined in a toroidal trap. In a recent theoretical paper Kanamoto, Saito, and Ueda have investigated the ground state and the low-lying excited states of such a system [5] (see also Ref. [7] for a detailed discussion of this problem). As shown, the Gross-Pitaevskii mean-field theory predicts a quantum phase transition between a uniform state and a localized state as the absolute value of the strength of the interaction inreases. Furthermore, numerical diagonalization of the Hamiltonian for a finite number of bosons shows that the transition in this case is smeared out, as expected in finite systems.In our study we examine the same problem using different techniques. Initially we use the mean-field approximation with a properly chosen variational wavefunction to study the phase transition and the order parameter in the two phases. Then, working in the same truncated space we use a Bogoliubov transformation to diagonalize the Hamiltonian. Having diagonalized the problem, we examine the lowest state of the system, the low-lying excited states, as well as the depletion of the condensate at the region of the transition. Our results are consistent with those of Ref. [5].Let us therefore consider a Bose-Einstein condensate in a toroidal trap. Following Ref.[5], we assume that the system contains N bosons, that the radius of the torus is R and its cross section is S = πr 2 , with r ≪ R. Ifψ(θ) is the field operator, the Hamiltonian iŝwhere U 0 = 8πaR/S, with a being the scattering length for elastic atom-atom collisions, and θ is the azimuthal angle. Here the length is measured in units of R and the energy in units ofh 2 /2mR 2 , with m being the atom mass. Let us start with the mean-field approach. Within this approximation the system is described by a single wavefunction, the order parameter ψ(r), and the many-body state is the product Π i ψ(r i ), with i = 1, . . . , N , where N is the number of atoms. Therefore this approximation ignores correlations between the atoms and in general it has a higher energy than the exact solution that one can get by diagonalizing the Hamiltonian.In this problem it is natural to work in the basis of plane-wave states φ l (θ) = e ilθ / √ 2π and according to the analysis of Ref.[5], the order parameter close to the transition consists of the stat...

show abstract

mentioning

confidence: 99%

Bose-Einstein condensates with attractive interactions on a ring

Kavoulakis¹

2003

Phys. Rev. A

View full text Add to dashboard Cite

show abstract

“…The NLS rigidly links the structure of a time-dependent solution to its initial form, with many features of the latter rendered identifiable in the former. In particular, a sudden increase of the strength of the attractive coupling constant by a factor of 4, i.e., an interaction quench, converts a fundamental soliton into an exact superposition of two solitons with zero relative velocity, zero spatial separation, and with a mass ratio 3∶1 [21][22][23]. The two superimposed solitons have different chemical potentials, hence, the density oscillates as a result of interference.…”

mentioning

confidence: 99%

Dissociation of One-Dimensional Matter-Wave Breathers due to Quantum Many-Body Effects

et al. 2017

View full text Add to dashboard Cite

We use the ab initio Bethe ansatz dynamics to predict the dissociation of one-dimensional cold-atom breathers that are created by a quench from a fundamental soliton. We find that the dissociation is a robust quantum many-body effect, while in the mean-field (MF) limit the dissociation is forbidden by the integrability of the underlying nonlinear Schrödinger equation. The analysis demonstrates the possibility to observe quantum many-body effects without leaving the MF range of experimental parameters. We find that the dissociation time is of the order of a few seconds for a typical atomic-soliton setting. DOI: 10.1103/PhysRevLett.119.220401 Under normal conditions, interacting quantum Bose gases do not readily exhibit signatures of their corpuscular nature, but rather follow the behavior predicted by meanfield (MF) theory. The observability of microscopic quantum effects involving a substantial fraction of the particles in a coherent macroscopic setting generally requires going beyond MF, for example, at low density in one dimension (1D) [1,2] or high density in three dimensions (3D). In 3D systems, the high-density Lee-Huang-Yang corrections, which are induced by quantum correlations, were realized experimentally using the Feshbach resonance [3] and in the spectacular form of "quantum droplets" in dipolar [4][5][6] and isotropic [7] bosonic gases, i.e., as self-trapped states stabilized against the collapse by the beyond-MF selfrepulsion. This stabilization was predicted in Refs. [8][9][10]. Quantum effects involving a macroscopic number of atoms in collapsing attractive 3D gases and colliding condensates were also observed [11][12][13][14][15] and analyzed [16,17] in the MF density range.A generic opportunity to observe beyond-MF effects arises when a particular symmetry of the MF dynamics, which prohibits a certain effect, is broken at the microscopic level, thus making observation of the effect possible. For instance, the scale invariance in the dynamics of a harmonically trapped 2D Bose gas nullifies the interaction-induced shift of the frequency of monopole excitations for all excitation amplitudes; however, this scale invariance is broken by the quantum many-body Hamiltonian, leading to a small shift, albeit discernible on a zero background [18]. In this context, the symmetry breaking by the secondary quantization may be considered as a manifestation of a general phenomenon known as the quantum anomaly [19]. In this Letter we develop a similar strategy for predicting beyond-MF effects in the one-dimensional (1D) self-attractive Bose gas in a MF range of parameters. The respective MF equation amounts to the nonlinear Schrödinger (NLS) equation, integrable by the inverse-scattering transform [20]. The NLS rigidly links the structure of a time-dependent solution to its initial form, with many features of the latter rendered identifiable in the former. In particular, a sudden increase of the strength of the attractive coupling constant by a factor of 4, i.e., an interaction quench, converts a fundamental s...

show abstract

“…Such an ansatz has been considered in [43,61,62], and is most appropriate in parameter regimes where the strength of the radial trap potential dominates over the strength of interactions, but the strength of interactions dominates over the strength of the axial trap potential. Following the above procedure, the variational energy expression now becomes,…”

Section: Variational Analysis: Sech Ansatzmentioning

confidence: 99%

“…The collapse instability has been investigated experimentally [15,[26][27][28]. Numerous theoretical studies have focused on identifying the parameters associated with the onset of collapse in condensates of various geometries, using variational [43,44,61,62,64], perturbative [24], and numerical [16,17,23,43,61,62,66] methods. The condensate dynamics during collapse are the subject of continuing theoretical study [30,[67][68][69][70].…”

Section: Collapse and The Critical Parametermentioning

confidence: 99%

Spontaneous Symmetry Breaking, Self-Trapping, and Josephson Oscillations

Malomed¹

2013

Progress in Optical Science and Photonics

View full text Add to dashboard Cite

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.

show abstract

Dynamics of a matter-wave bright soliton in an expulsive potential

Cited by 146 publications

References 32 publications

Bose-Einstein condensates with attractive interactions on a ring

Bose-Einstein condensates with attractive interactions on a ring

Dissociation of One-Dimensional Matter-Wave Breathers due to Quantum Many-Body Effects

Spontaneous Symmetry Breaking, Self-Trapping, and Josephson Oscillations

Contact Info

Product

Resources

About