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arXiv:1408.2440

Signature of existence of a BEC-type state in a dilute gas above the BEC transition temperature

Yinbiao Yang, Wen-ge Wang

Published Aug 8, 2014• 0 citations
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Abstract

We study quantum coherence properties of a dilute gas at temperatures above, but not much above the transition temperature of Bose-Einstein condensation (BEC). In such a gas, a small proportion of the atoms may possess coherence lengths longer than the mean neighboring-atomic distance, implying the existence of quantum coherence more than that expected for thermal atoms. Conjecturing that a part of this proportion of the atoms may lie in a BEC-type state, some unexplained experimental results [Phys. Rev. A, 71, 043615 (2005)] can be explained.

DOI
10.48550/arxiv.1408.2440

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We study quantum coherence properties of a dilute gas at temperatures above, but not much above the transition temperature of Bose-Einstein condensation (BEC). In such a gas, a small proportion of the atoms may possess coherence lengths longer than the mean neighboring-atomic distance, implying the existence of quantum coherence more than that expected for thermal atoms. Conjecturing that a part of this proportion of the atoms may lie in a BEC-type state, some unexplained experimental results [Phys. Rev. A, 71, 043615 (2005)] can be explained.
We study quantum coherence properties of a dilute gas at temperatures above, but not much above, the transition temperature of Bose-Einstein condensation. In such a gas, a small proportion of the atoms may possess coherence lengths longer than the mean neighboring-atomic distance, implying the existence of quantum coherence greater than that expected for thermal atoms. Conjecturing that a part of this proportion of the atoms may lie in a coherently condensed state, some unexplained experimental results [D. E. Miller et al., Phys. Rev. A 71, 043615 (2005)] can be explained.
We reconcile a long-standing controversy regarding the transition temperature of the Bose-Einstein condensation in a dilute interacting Bose gas, by showing that there is a crossover between ideal gas and interacting gas. The former corresponds to a Knudsen (or collisionless) regime, in which the mean-free-path is much larger than the system dimension, while the latter corresponds to the opposite hydrodynamic regime. The deviation of the transition temperature from that of the non-interacting gas is proportional to the square root of a in the Knudsen regime, and to a in the hydrodynamic regime, where a is the scattering length. This crossover may be observable in a Bose gas trapped in a potential or on an optical lattice.
We report observation of Bose-Einstein condensation (BEC) of a trapped, dilute gas of atomic hydrogen. The condensate and normal gas are studied by two-photon spectroscopy of the 1S1S1S- 2S2S2S transition. Interactions among the atoms produce a shift of the resonance frequency proportional to density. The condensate is clearly distinguished by its large frequency shift. The peak condensate density is $4.8\ifmmode\pm\else\textpm\fi{}1.1\ifmmode\times\else\texttimes\fi{}{10}^{15}{\mathrm{cm}}^{\ensuremath{-}3}$, corresponding to a condensate population of 109{10}^{9}109 atoms. The BEC transition occurs at about $T\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}50\ensuremath{\mu}\mathrm{K}$ and $n\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}1.8\ifmmode\times\else\texttimes\fi{}{10}^{14}{\mathrm{cm}}^{\ensuremath{-}3}$.
Summary form only given. Bose-Einstein condensation (BEG) has been observed in a dilute gas of sodium atoms. A Bose-Einstein condensate consists of a macroscopic population of the ground state of the system and is a coherent state of matter. In an ideal gas, this phase transition is purely quantum statistical. The study of BEC in weakly interacting systems that can be controlled and observed with precision holds the promise of revealing new macroscopic quantum phenomena that can be understood from first principles.