Short-Distance Correlation Properties of the Lieb-Liniger System and Momentum Distributions of Trapped One-Dimensional Atomic Gases

Abstract

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/p^4 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.

arXiv commentA significant misprint in the definition of c_2 is corrected. 5 pages, 1 EPS figure, references updated

References in corpus (17)

• Quantum phase transition from a superfluid to a Mott insulator in a gas of ultracold atoms
• Atomic Scattering in Presence of an External Confinement and a Gas of Impenetrable Bosons
• Formation and Propagation of Matter Wave Soliton Trains
• Dark Solitons in Bose-Einstein Condensates
• Realization of Bose-Einstein condensates in lower dimensions
• A quasi-pure Bose-Einstein condensate immersed in a Fermi sea
• Quantum Inverse Scattering Method and Correlation Functions
• Regimes of quantum degeneracy in trapped 1D gases
• Bosons in cigar-shape traps: Thomas-Fermi regime, Tonks-Girardeau regime, and between
• Stability and phase coherence of trapped 1D Bose gases
• Ground state properties of a one-dimensional condensate of hard core bosons in a harmonic trap
• Finite one dimensional impenetrable Bose systems: Occupation numbers
• High-momentum tail in the Tonks gas under harmonic confinement
• Phase fluctuations in atomic Bose gases
• Local correlations in a strongly interacting 1D Bose gas
• Ground-state properties of hard core bosons in one-dimensional harmonic traps
• Time and Temperature Dependent Correlation Functions of 1D Models of Quantum Statistical Mechanics

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