Production of Two Overlapping Bose-Einstein Condensates by Sympathetic Cooling

Myatt, C. J.; Burt, Eric A.; Ghrist, R. W.; Cornell, Eric A.; Wieman, C. E.

doi:10.1142/9789812813787_0066

Cited by 27 publications

(42 citation statements)

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“…Although the theories and numerical methods presented here apply to multi-component BEC with any number of components [43,40,1,28,30], we concentrate here on two-component BEC for simplicity [28,29,42,33]. At temperatures T much smaller than the critical temperature T c [44,20], in the rotating frame, a two-component BEC with an external driving field can be well described by two self-consistent nonlinear Schrödinger equations (NLSEs), also known as coupled Gross-Pitaevskii equations (CGPEs) [32,22,37,36],…”

Section: Introductionmentioning

confidence: 99%

Analysis and efficient computation for the dynamics of two-component Bose-Einstein condensates

Bao¹

2008

Stationary and Time Dependent Gross-Pitaevskii Equations

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Abstract. In this paper, we review some recent results on the analysis and efficient computation for the dynamics of rotating two-component Bose-Einstein condensates (BECs). We begin with the three-dimensional (3D) coupled GrossPitaevskii equations (GPEs) with an angular momentum rotation term and an external driving field, show how to scale it into dimensionless form, reduce it to a 2D and 1D GPE in the limiting regime of strong anisotropic confinement and present its semiclassical scaling and geometric optics. Dynamic laws on the angular momentum expectation, density of each component, condensate widths and analytical solutions of stationary states with its center shifted from the trapping center are presented. In addition, efficient and accurate numerical methods for computing the dynamics of rotating two-component BEC are presented and some numerical results are reported to demonstrate the efficiency and accuracy of the numerical methods.

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Section: Introductionmentioning

confidence: 99%

Analysis and efficient computation for the dynamics of two-component Bose-Einstein condensates

Bao¹

2008

Stationary and Time Dependent Gross-Pitaevskii Equations

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“…Recently, BEC with multiple species have been realized in experiments [17,18,25,26,28,32,34] and some interesting phenomenona absent in single-component BEC were observed in experiments and studied in theory [2,6,7,9,16,20,24]. The simplest multi-component BEC is the binary mixture, which can be used as a model for producing coherent atomic beams (also called atomic laser) [30,31].…”

Section: Introductionmentioning

confidence: 99%

“…The simplest multi-component BEC is the binary mixture, which can be used as a model for producing coherent atomic beams (also called atomic laser) [30,31]. The first experiment for two-component BEC was performed in JILA with |F = 2, m f = 2〉 and |1, −1〉 spin states of 87 Rb [28]. Since then, extensive experimental and theoretical studies of two-component BEC have been carried out in the last several years [3,10,19,27,35,38].…”

Section: Introductionmentioning

confidence: 99%

Ground States of Two-component Bose-Einstein Condensates with an Internal Atomic Josephson Junction

Bao

Cai

2011

E Asian J Appl Math

119

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Abstract. In this paper, we prove existence and uniqueness results for the ground states of the coupled Gross-Pitaevskii equations for describing two-component Bose-Einstein condensates with an internal atomic Josephson junction, and obtain the limiting behavior of the ground states with large parameters. Efficient and accurate numerical methods based on continuous normalized gradient flow and gradient flow with discrete normalization are presented, for computing the ground states numerically. A modified backward Euler finite difference scheme is proposed to discretize the gradient flows. Numerical results are reported, to demonstrate the efficiency and accuracy of the numerical methods and show the rich phenomena of the ground sates in the problem.

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“…They are used e.g. for preliminary cooling in the Bose-Einstein condensation [17][18][19]. In recognition of their pioneering achievements in the cooling and trapping of atoms in 1997, C. Cohen-Tannoudji, S. Chu and W. Phillips were awarded the Nobel Prize [20].…”

Section: Introductionmentioning

confidence: 99%