Dark solitons as quasiparticles in trapped condensates

Brazhnyi, V. A.; Konotop, V. V.; Pitaevskiĭ, Lev P.

doi:10.1103/physreva.73.053601

Cited by 56 publications

(83 citation statements)

References 26 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In fact, this equation is expected to be valid as long as the number of atoms exceeds a certain minimum value (typically much larger than 10), for which oscillations in the density profiles become essentially suppressed [151,154,158]; in other words, the density variations should occur on a length scale which is larger than the Fermi healing length ξ F ≡ 1/(πρ p ) (where ρ p is the peak density of the trapped gas). The quintic NLS model has been used in various studies [151,[159][160][161], basically connected to the dynamics of dark solitons in the Tonks-Girardeau gas, and in the aforementioned crossover regime of γ ∼ O(1) [150]. In this connection, it is relevant to note that in the above works it was found that, towards the strongly-interacting regime, the dark soliton oscillation frequency is up-shifted, which may be used as a possible diagnostic tool of the system being in a particular interaction regime.…”

Section: Weakly-and Strongly-interacting 1d Bose Gases the Tonks-girmentioning

confidence: 99%

Nonlinear waves in Bose–Einstein condensates: physical relevance and mathematical techniques

2008

View full text Add to dashboard Cite

Abstract. The aim of the present review is to introduce the reader to some of the physical notions and of the mathematical methods that are relevant to the study of nonlinear waves in Bose-Einstein Condensates (BECs). Upon introducing the general framework, we discuss the prototypical models that are relevant to this setting for different dimensions and different potentials confining the atoms. We analyze some of the model properties and explore their typical wave solutions (plane wave solutions, bright, dark, gap solitons, as well as vortices). We then offer a collection of mathematical methods that can be used to understand the existence, stability and dynamics of nonlinear waves in such BECs, either directly or starting from different types of limits (e.g., the linear or the nonlinear limit, or the discrete limit of the corresponding equation). Finally, we consider some special topics involving more recent developments, and experimental setups in which there is still considerable need for developing mathematical as well as computational tools.PACS numbers: 03.75. Kk, 03.75.Lm, 05.45 • EP: Ermakov-Pinney (Equation)• GP: Gross-Pitaevskii (Equation)• KdV: Korteweg-de Vries (Equation)• LS: Lyapunov-Schmidt (Technique)• MT: Magnetic Trap• NLS: Nonlinear Schrödinger (Equation)• NPSE: Non-polynomial Schrödinger Equation IntroductionThe phenomenon of Bose-Einstein condensation is a quantum phase transition originally predicted by Bose [1] and Einstein [2,3] in 1924. In particular, it was shown that below a critical transition temperature T c , a finite fraction of particles of a boson gas (i.e., whose particles obey the Bose statistics) condenses into the same quantum state, known as the Bose-Einstein condensate (BEC). Although BoseEinstein condensation is known to be a fundamental phenomenon, connected, e.g., to superfluidity in liquid helium and superconductivity in metals (see, e.g., Ref.[4]), BECs were experimentally realized 70 years after their theoretical prediction: this major achievement took place in 1995, when different species of dilute alkali vapors confined in a magnetic trap (MT) were cooled down to extremely low temperatures [5][6][7], and has already been recognized through the 2001 Nobel prize in Physics [8,9]. This first unambiguous manifestation of a macroscopic quantum state in a manybody system sparked an explosion of activity, as reflected by the publication of several thousand papers related to BECs since then. Nowadays there exist more than fifty experimental BEC groups around the world, while an enormous amount of theoretical work has followed and driven the experimental efforts, with an impressive impact on many branches of Physics.From a theoretical standpoint, and for experimentally relevant conditions, the static and dynamical properties of a BEC can be described by means of an effective mean-field equation known as the Gross-Pitaevskii (GP) equation [10,11]. This is a variant of the famous nonlinear Schrödinger (NLS) equation [12] (incorporating an external potential used to confine th...

show abstract

Section: Weakly-and Strongly-interacting 1d Bose Gases the Tonks-girmentioning

confidence: 99%

Nonlinear waves in Bose–Einstein condensates: physical relevance and mathematical techniques

2008

View full text Add to dashboard Cite

show abstract

“…In this case we can formulate the problem of motion of a dark soliton "in the potential" V (x) in terms of its collective coordinate. This problem has been addressed in several papers (see, e.g., [13,14,15,16,17,18,19]) where it was shown that the dynamics of dark solitons is quite nontrivial. In particular, if a BEC described by the standard GP equation (2) is confined in a harmonic axial trap,…”

Section: Introductionmentioning

confidence: 99%

“…To estimate the first term of the series expansion of E with respect to v 2 , we split the integral (26) into two terms (see [16]),…”

Section: Small Amplitude Oscillations Of a Deep Solitonmentioning

confidence: 99%

“…Our theory will be based on the elegant approach of Refs. [15,16] where the dark soliton was considered as a "Landau quasi-particle" whose motion in the stationary potential V (x) is governed by the quasi-particle's "energy conservation" law in close analogy with the Newtonian particle motion. The generalization of this approach to arbitrary f (ρ) allows us to derive the equation of motion of the dark soliton for the general case and to show the dependence of the soliton effective mass on the system parameters.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Dark soliton oscillations in Bose–Einstein condensates with multi-body interactions

Камчатнов¹,

Salerno²

2009

J. Phys. B: At. Mol. Opt. Phys.

View full text Add to dashboard Cite

Abstract. We consider the dynamics of dark matter solitons moving through nonuniform cigar-shaped Bose-Einstein condensates described by the mean field GrossPitaevskii equation with generalized nonlinearities, in the case when the condition for the modulation stability of the Bose-Einstein condensate is fulfilled. The analytical expression for the frequency of the oscillations of a deep dark soliton is derived for nonlinearities which are arbitrary functions of the density, while specific results are discussed for the physically relevant case of a cubic-quintic nonlinearity modeling twoand three-body interactions, respectively. In contrast to the cubic Gross-Pitaevskii equation for which the frequencies of the oscillations are known to be independent of background density and interaction strengths, we find that in the presence of a cubicquintic nonlinearity an explicit dependence of the oscillations frequency on the above quantities appears. This dependence gives rise to the possibility of measuring these quantities directly from the dark soliton dynamics, or to manage the oscillation via the changes of the scattering lengths by means of Feshbach resonance. A comparison between analytical results and direct numerical simulations of the cubic-quintic GrossPitaevskii equation shows good agreement which confirms the validity of our approach.

show abstract

“…The steps of our analysis, and the structure of our presentation, are as follows. First, starting from a DGPE which encompasses the above potentials (linear and periodic), we employ two different analytical approaches: dark-soliton perturbation theory [2,[48][49][50] and the so-called Landau dynamics approach [51,52]; both analytical techniques lead to an equation of motion for the ensuing dynamics of the soliton center position (Sec. II).…”

Section: Introductionmentioning

confidence: 99%

Finite-temperature dynamics of matter-wave dark solitons in linear and periodic potentials: An example of an antidamped Josephson junction

et al. 2012

View full text Add to dashboard Cite

We study matter-wave dark solitons in atomic Bose-Einstein condensates (BECs) at finite temperatures, under the effect of linear and periodic potentials. Our model, namely, a dissipative Gross-Pitaevskii equation, is treated analytically by means of dark-soliton perturbation theory and the Landau dynamics approach, which result in a Newtonian equation of motion for the dark-soliton center. This reduced model, which incorporates an effective washboard potential and an antidamping term accounting for finite-temperature effects, constitutes an example of an antidamped Josephson junction. We perform a qualitative (local and global) analysis of the equation of motion. We present results of systematic numerical simulations for both zero-and finite-temperature BECs to highlight the differences between the Hamiltonian and dissipative settings. For sufficiently small wave numbers of the periodic potential and weak linear potentials, the analytical results are found to be in good agreement with pertinent ones obtained via a Bogoliubov-de Gennes analysis and direct numerical simulations.

show abstract

Dark solitons as quasiparticles in trapped condensates

Cited by 56 publications

References 26 publications

Nonlinear waves in Bose–Einstein condensates: physical relevance and mathematical techniques

Nonlinear waves in Bose–Einstein condensates: physical relevance and mathematical techniques

Dark soliton oscillations in Bose–Einstein condensates with multi-body interactions

Finite-temperature dynamics of matter-wave dark solitons in linear and periodic potentials: An example of an antidamped Josephson junction

Contact Info

Product

Resources

About