Bose-Einstein condensation of lithium

Sackett, C. A.; Bradley, C. C.; Welling, Matthias; Hulet, Randall G.

doi:10.1007/s003400050293

Cited by 59 publications

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“…The study of these effects on the dynamics of the condensate is the main topic of this Letter. Some preliminary results have already appeared in a recent review article [16].…”

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confidence: 95%

“…The study of these effects on the dynamics of the condensate is the main topic of this Letter. Some preliminary results have already appeared in a recent review article [16].When collisions can be neglected, the dynamics of the condensate wave function c for a gas with a , 0 is well described by the nonlinear Schrödinger (or Gross-Here m denotes the mass of 7 Li, T 2B ͑0, 0; 0͒ 4pah 2 ͞m is the two-body T matrix, and a is the scattering length of 227a 0 [18]. For the external trapping potential V ͑x͒ we take a harmonic potential with an effective isotropic level splittinghv h͑v x v y v z ͒ 1͞3 of 7 nK [8].…”

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confidence: 96%

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Growth and Collapse of a Bose-Einstein Condensate with Attractive Interactions

1998

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We consider the dynamics of a quantum degenerate trapped gas of 7 Li atoms. Because the atoms have a negative s-wave scattering length, a Bose condensate of 7 Li becomes mechanically unstable when the number of condensate atoms approaches a maximum value. We calculate the dynamics of the collapse that occurs when the unstable point is reached. In addition, we use the quantum Boltzmann equation to investigate the nonequilibrium kinetics of the atomic distribution during and after evaporative cooling. The condensate is found to undergo many cycles of growth and collapse before a stationary state is reached. [S0031-9007(98) show in this paper that the dynamical behavior of a negative scattering length gas, such as 7 Li, is especially interesting, and offers the opportunity to directly observe and study macroscopic quantum tunneling.A negative scattering length a implies effectively attractive interactions. In a spatially homogeneous gas, these interactions lead to ordinary classical condensation into a liquid or solid, preventing Bose-Einstein condensation in the metastable region of the phase diagram [5]. However, confinement in an atom trap produces stabilizing forces that enable the formation of a metastable BoseEinstein condensate, if the number of condensed atoms is less than some maximum number N m . For a harmonic trap, Ruprecht et al. [6] showed that in mean-field theory N m Ӎ 0.57l͞jaj, where l ͑h͞mv͒ 1͞2 is the extent of the one-particle ground state in the harmonic trap [7]. For the 7 Li experiments of Ref. [8], N m Ӎ 1400 atoms, which agrees with the measured value.Although a condensate can exist in a trapped gas, it is predicted to be metastable and to decay by quantum or thermal fluctuations [9][10][11]. The condensate has only one unstable collective mode, which in the case of an isotropic trap corresponds to the breathing mode [12,13]. The condensate therefore collapses as a whole, either by thermal excitation over or by quantum mechanical tunneling through a macroscopic energy barrier in configuration space. The probability of forming small, dense clusters is greatly suppressed because of the large energy barrier for this process, compared to that for the breathing mode. This suppression can also be understood from the fact that the typical length scale for fluctuations of the condensate is the healing length, which is approximately equal to the condensate size near the instability point.Experimentally, it is also important to understand how such a condensate can be formed from a noncondensed cloud by means of evaporative cooling. This question was recently addressed by Gardiner et al. in the context of experiments with gases having a . 0 [14]. These authors neglect the coherent dynamics of the condensate and focus instead on the kinetics of condensation [15]. By treating the noncondensed atoms as a static "heat bath," they are able to derive a simple equation for the growth of the number of condensate particles that appears to fit well with experimental results [4]. The same approach, however, doe...

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“…The study of these effects on the dynamics of the condensate is the main topic of this Letter. Some preliminary results have already appeared in a recent review article [16].…”

mentioning

confidence: 95%

mentioning

confidence: 96%

Growth and Collapse of a Bose-Einstein Condensate with Attractive Interactions

1998

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“…When the volume and temperature are held fixed, according to grand ensemble theory the equation of state is given by 29,30 …”

Section: B Equation Of State Near Z =mentioning

confidence: 99%

“…or using the binomial theorem as well as (19), we express the pressure and particle density in the familiar form of the Mayer expansions, 29,30 by writing them as…”

Section: One-dimensional Interacting Bose Gasmentioning

confidence: 99%

“…Not long after the development of these experimental techniques the observation of BEC was achieved. 1,3,30 To make accurate predictions concerning the behavior of quantum systems in such environments requires more complex analyses than those for the free ideal gases. As a consequence, much recent work in mathematical physics has been devoted to deriving approximate analytic expressions for the thermodynamic properties of both Bose and Fermi gases trapped by external potentials.…”

Section: Ideal Bose Gases In a Harmonic Potentialmentioning

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D-dimensional Bose gases and the Lambert W function

Tanguay

Gil

Jeffrey

et al. 2010

Journal of Mathematical Physics

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The applications of the Lambert W function (also known as the W function) to D-dimensional Bose gases are presented. We introduce two sets of families of logarithmic transcendental equations that occur frequently in thermodynamics and statistical mechanics and present their solution in terms of the W function. The low temperature T behavior of free ideal Bose gases is considered in three and four dimensions. It is shown that near condensation in four dimensions, the chemical potential μ and pressure P can be expressed in terms of T through the W function. The low T behavior of one-and two-dimensional ideal Bose gases in a harmonic trap is studied. In 1D, the W function is used to express the condensate temperature, T C , in terms of the number of particles N ; in 2D, it is used to express μ in terms of T . In the low T limit of the 1D hard-core and the 3D Bose gas, T can be expressed in terms of P and μ through the W function. Our analysis allows for the possibility to consider μ, T , and P as complex variables. The importance of the underlying logarithmic structure in ideal quantum gases is seen in the polylogarithmic and W function expressions relating thermodynamic variables such as μ, T , and P. C

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Field Theory for Trapped Atomic Gases

Stoof

Les Houches - Ecole D’Ete De Physique Theorique

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In this course we give a selfcontained introduction to the quantum field theory for trapped atomic gases, using functional methods throughout. We consider both equilibrium and nonequilibrium phenomena. In the equilibrium case, we first derive the appropriate Hartree-Fock theory for the properties of the gas in the normal phase. We then turn our attention to the properties of the gas in the superfluid phase, and present a microscopic derivation of the Bogoliubov and Popov theories of Bose-Einstein condensation and the Bardeen-Cooper-Schrieffer theory of superconductivity. The former are applicable to trapped bosonic gases such as rubidium, lithium, sodium and hydrogen, and the latter in particular to the fermionic isotope of atomic lithium. In the nonequilibrium case, we discuss various topics for which a field-theoretical approach is especially suited, because they involve physics that is not contained in the Gross-Pitaevskii equation. Examples are quantum kinetic theory, the growth and collapse of a Bose condensate, the phase dynamics of bosonic and fermionic superfluids, and the collisionless collective modes of a Bose gas below the critical temperature.

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Bose-Einstein condensation of lithium

Cited by 59 publications

References 1 publication

Growth and Collapse of a Bose-Einstein Condensate with Attractive Interactions

Growth and Collapse of a Bose-Einstein Condensate with Attractive Interactions

D-dimensional Bose gases and the Lambert W function

Field Theory for Trapped Atomic Gases

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