Atom-interferometric study of Bose-Einstein condensation

Altenmüller, Thomas; Müller, Rainer; Schenzle, A.

doi:10.1103/physreva.56.2959

Cited by 10 publications

(15 citation statements)

References 10 publications

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“…Going beyond the second order term, thus recovering the full T-matrix including statistical corrections, becomes a very difficult task, which has still not been fully accomplished. This standpoint has been considered in [57,58,42,49].…”

Section: Survey and Comparison Of Derivations In The Literaturementioning

confidence: 99%

Quantum linear Boltzmann equation

2009

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We review the quantum version of the linear Boltzmann equation, which describes in a non-perturbative fashion, by means of scattering theory, how the quantum motion of a single test particle is affected by collisions with an ideal background gas. A heuristic derivation of this Lindblad master equation is presented, based on the requirement of translation-covariance and on the relation to the classical linear Boltzmann equation. After analyzing its general symmetry properties and the associated relaxation dynamics, we discuss a quantum Monte Carlo method for its numerical solution. We then review important limiting forms of the quantum linear Boltzmann equation, such as the case of quantum Brownian motion and pure collisional decoherence, as well as the application to matter wave optics. Finally, we point to the incorporation of quantum degeneracies and self-interactions in the gas by relating the equation to the dynamic structure factor of the ambient medium, and we provide an extension of the equation to include internal degrees of freedom.Comment: 63 pages, 6 figures; v3:corresponds to published versio

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Section: Survey and Comparison Of Derivations In The Literaturementioning

confidence: 99%

Quantum linear Boltzmann equation

2009

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“…This is precisely what would be expected, since the second calculation requires the assumption of weak interaction; it thus serves to confirm the ε = 1 result of the first. Neither of these is the most elegant or general calculation one could imagine; the first is rather cumbersome, and the second would be neater if generalized to second quantized form [5]. But the first has the advantage of displaying the physics of decoherence in an almost pictorial way, while allowing a calculation involving the full scattering amplitude.…”

Section: Introductionmentioning

confidence: 99%

Collisional decoherence reexamined

2003

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We re-derive the quantum master equation for the decoherence of a massive Brownian particle due to collisions with the lighter particles from a thermal environment. Our careful treatment avoids the occurrence of squares of Dirac delta functions. It leads to a decoherence rate which is smaller by a factor of 2 pi compared to previous findings. This result, which is in agreement with recent experiments, is confirmed by both a physical analysis of the problem and by a perturbative calculation in the weak coupling limit.Comment: 33 pages, 4 figure

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“…The calculation of collisional decoherence was initiated by Joos and Zeh [1], with generalizations of their result and corrections to the overall normalization given in papers of Gallis and Fleming [2], Dodd and Halliwell [3], and Hornberger and Sipe [4]. An even more general calculation of collisional decoherence was also given by Diósi [5], but this was not known to Hornberger and Sipe, while noted by Dodd and Halliwell, as well as in the master equation papers of Altenmüller, Müller, and Schenzle [6] and of Vacchini [7]. A difficulty encountered in refs [1], [2], and [4] is the appearance of a squared delta function of the absolute value of momentum in the calculation of the decoherence rate.…”

Section: Introductionmentioning

confidence: 99%

Normalization of collisional decoherence: squaring the delta function, and an independent cross-check

Adler

2006

J. Phys. A: Math. Gen.

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We show that when the Hornberger-Sipe calculation of collisional decoherence is carried out with the squared delta function a delta of energy instead of a delta of the absolute value of momentum, following a method introduced by Diósi, the corrected formula for the decoherence rate is simply obtained. The results of Hornberger and Sipe and of Diósi are shown to be in agreement. As an independent cross-check, we calculate the mean squared coordinate diffusion of a hard sphere implied by the corrected decoherence master equation, and show that it agrees precisely with the same quantity as calculated by a classical Brownian motion analysis.

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Atom-interferometric study of Bose-Einstein condensation

Cited by 10 publications

References 10 publications

Quantum linear Boltzmann equation

Quantum linear Boltzmann equation

Collisional decoherence reexamined

Normalization of collisional decoherence: squaring the delta function, and an independent cross-check

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