Phys. Rev. Lett. 91, 090401 (2003) [4 pages]Short-Distance Correlation Properties of the Lieb-Liniger System and Momentum Distributions of Trapped One-Dimensional Atomic GasesReceived 29 October 2002; published 26 August 2003 We derive exact closed-form expressions for the first few terms of the short-distance Taylor expansion of the one-body correlation function of the Lieb-Liniger gas. As an intermediate result, we obtain the high-p asymptotics of the momentum distribution of both free and harmonically trapped atoms and show that it obeys a universal 1/p4 law for all values of the interaction strength. We discuss the ways to observe the predicted momentum distributions experimentally, regarding them as a sensitive identifier for the Tonks-Girardeau regime of strong correlations. © 2003 The American Physical Society URL:
http://link.aps.org/doi/10.1103/PhysRevLett.91.090401
DOI:
10.1103/PhysRevLett.91.090401
PACS:
05.30.Jp, 02.30.Ik, 03.75.–b
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