Short-distance correlation properties of the Lieb-Liniger system and momentum distributions of trapped one-dimensional atomic gases

Phys Rev Lett. 2003 Aug 29;91(9):090401. doi: 10.1103/PhysRevLett.91.090401. Epub 2003 Aug 26.


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.