Ground-state properties of trapped Bose-Einstein condensates: Extension of the Thomas-Fermi approximation

Mateo, A. Muñoz; Delgado, V.

doi:10.1103/physreva.75.063610

Cited by 49 publications

(88 citation statements)

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“…[9] a hysteresis loop has been observed in the generation of quantized persistent currents by means of a rotating weak link. A 3D ring of Bose-condensed 23 Na atoms was prepared in a stationary state with winding number 0 (1), and the frequency Ω , showing a big discrepancy. As the intensity of the link decreases, the size of the loop becomes considerably smaller in the experiment than in the numerics.…”

Section: Introductionmentioning

confidence: 99%

Persistent currents supported by solitary waves in toroidal Bose-Einstein condensates

et al. 2015

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We analyze the generation of persistent currents in Bose-Einstein condensates of ultracold gases confined in a ring. This phenomenon has been recently investigated in an experiment [Nature 506, 200 (2014)], where hysteresis loops have been observed in the activation of quantized persistent currents by rotating weak links. In this work, we demonstrate the existence of 3D stationary currents with non-quantized angular momentum. They are generated by families of solitary waves that show a continuous variation in the angular momentum, and provide a bridge between different winding numbers. We show that the size of hysteresis loops is determined by the range of existence within the weak link region of solitary waves which configure the energy barrier preventing phase slips. The barrier vanishes when the critical rotation leads winding numbers and solitonic states to a matching configuration. At this point, Landau and Feynman criteria for phase slips meet: the fluid flow reaches the local speed of sound, and stationary vortex lines (which are the building blocks of solitons) can be excited inside the system.

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Section: Introductionmentioning

confidence: 99%

Persistent currents supported by solitary waves in toroidal Bose-Einstein condensates

et al. 2015

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“…The transverse chemical potential µ r of an elongated condensate was also derived recently by Muñoz Mateo and Delgado [118] as a function of the longitudinal density ρ. This way, the same authors presented in the recent work of Ref.…”

Section: Mean-field Models With Non-cubic Nonlinearitiesmentioning

confidence: 99%

“…Following Refs. [115][116][117][118][119], one may factorize the wavefunction as per Eq. (20), but with the transverse wavefunction Φ depending also on the longitudinal variable z.…”

Section: Mean-field Models With Non-cubic Nonlinearitiesmentioning

confidence: 99%

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

2008

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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...

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“…The first experimental achievement of it came before twenty two years by different experimental groups (Anderson et al, 1995;Davis et al, 1995;Bradley et al, 1995). This achievement had increased the interest in analyzing different aspects related to this phenomenon (Baym & Pethick, 1996;Fetter, 2009;Mateo & Delgado, 2007). Different theoretical approaches have been used to study these systems that undergoes Bose-Einstein condensation.…”

Section: Introductionmentioning

confidence: 99%

Bose-Einstein Condensation of Confined Atomic Gases at Ultra Low Temperatures

Serhan¹

2017

APR

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In this work I solve the Gross-Pitaevskii equation describing an atomic gas confined in an isotropic harmonic trap by introducing a variational wavefunction of Gaussian type. The chemical potential of the system is calculated and the solutions are discussed in the weakly and strongly interacting regimes. For the attractive system with negative scattering length the maximum number of atoms that can be put in the condensate without collapse begins is calculated

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Ground-state properties of trapped Bose-Einstein condensates: Extension of the Thomas-Fermi approximation

Cited by 49 publications

References 30 publications

Persistent currents supported by solitary waves in toroidal Bose-Einstein condensates

Persistent currents supported by solitary waves in toroidal Bose-Einstein condensates

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

Bose-Einstein Condensation of Confined Atomic Gases at Ultra Low Temperatures

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