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

摘要

We derive exact closed form expressions for the first few terms of theshort-distance Taylor expansion of the one-body correlation function of theLieb-Liniger gas. As an intermediate result we obtain the high-p asymptotics ofthe momentum distribution of both free and harmonically trapped atoms and showthat it obeys a universal 1/p^4 law for_all_ values of the interactionstrength. We discuss the ways to observe the predicted momentum distributionsexperimentally, regarding them as a sensitive identifier for theTonks-Girardeau regime of strong correlations.