Extension of Bogoliubov theory to quasicondensates

Mora, Christophe; Castin, Yvan

doi:10.1103/physreva.67.053615

Cited by 321 publications

(581 citation statements)

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“…As discussed in Ref. [16], l is chosen such that the healing length ξ ≡ / √ 2mgn and the thermal de Broglie wavelength, λ = 2π 2 /mk B T shows the predictions for three different radii, in particular 10 µm, 20 µm, and 30 µm. As the radius is increased, the heating rate due to a circular motion slowly recovers the heating rate for a linear motion.…”

Section: Simulation Methodsmentioning

confidence: 99%

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Probing superfluidity of Bose-Einstein condensates via laser stirring

et al. 2016

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We investigate the superfluid behavior of a Bose-Einstein condensate of 6 Li molecules. In the experiment by Weimer et al., Phys. Rev. Lett. 114, 095301 (2015) a condensate is stirred by a weak, red-detuned laser beam along a circular path around the trap center. The rate of induced heating increases steeply above a velocity vc, which we define as the critical velocity. Below this velocity, the moving beam creates almost no heating. In this paper, we demonstrate a quantitative understanding of the critical velocity. Using both numerical and analytical methods, we identify the non-zero temperature, the circular motion of the stirrer, and the density profile of the cloud as key factors influencing the magnitude of vc. A direct comparison to the experimental data shows excellent agreement.

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Section: Simulation Methodsmentioning

confidence: 99%

“…It was demonstrated in Ref. [7], that the onset of heating is governed by thermally activated phase arXiv:1509.02168v2 [cond-mat.quant-gas] 16 Oct 2015 slips, due to vortices traversing the barrier region. Recently, superfluidity was observed in an elongated 6 Li gas oscillating with respect to a 7 Li BEC [8].…”

Section: Introductionmentioning

confidence: 99%

Probing superfluidity of Bose-Einstein condensates via laser stirring

et al. 2016

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“…The strongly anisotropic cases with ω z ≪ ω r or ω r ≪ ω z are particularly interesting as they are related to effectively quasi one-dimensional (1D) and quasi two-dimensional (2D) BECs, respectively. Such lower dimensional BECs have been studied theoretically [92][93][94][95][96][97][98] (see also Ref. [51] for a rigorous mathematical analysis) and have been realized experimentally in optical and magnetic traps [99], in optical lattice potentials [100][101][102][103] and surface microtraps [78,79].…”

Section: Small-amplitude Linear Excitationsmentioning

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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“…Several experimental groups [4,5,6,7] are now interested in quasi-2D configurations using optical and magnetooptical traps which are expected to be more flexible for varying physical parameters such as the atomic density or the interaction strength. On the theoretical side, the general formalisms deeply differ from usual many body treatments in that they take into account both thermal phase fluctuations and the specific scattering properties [8,9,10,11,12,13].…”

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Variational approach for the two-dimensional trapped Bose-Einstein condensate

Pricoupenko

2004

Phys. Rev. A

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We construct a many-body Gaussian variational approach for the two-dimensional trapped Bose gas in the condensate phase. Interaction between particles is modelized by a generalized pseudopotential of zero range that allows recovering perturbative results in the ultra-dilute limit, while back action of non-condensate particles on the condensate part is taken into account for higher density. As an application, we derive the equation of state and solve stability problems encountered in similar mean-field formalisms for a single vortex configuration.

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Extension of Bogoliubov theory to quasicondensates

Cited by 321 publications

References 29 publications

Probing superfluidity of Bose-Einstein condensates via laser stirring

Probing superfluidity of Bose-Einstein condensates via laser stirring

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

Variational approach for the two-dimensional trapped Bose-Einstein condensate

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