Momentum distribution and non-local high order correlation functions of 1D strongly interacting Bose gas

Abstract

The Bethe ansatz, which was introduced in 1931 by Hans Bethe, has become a powerful method to obtain exact solu tions of one-dimensional (1D) quantum many-body systems. In 1963, Lieb and Liniger[1] solved the 1D many-particle problem of δ-function interacting bosons by the Bethe’s hy pothesis. The ground state, the momentum, and the elemen tary excitations were obtained for this model by using the Lieb–Liniger solution. In this context, a significant step was made on the discovery of the grand canonical description of this Lieb–Liniger model by Yang and Yang in 1969.[2] Now, this grand canonical approach is called Yang–Yang thermody namic method. The Yang–Yang thermodynamics of the Lieb– Liniger Bose gas provides benchmark understanding of quan tum statistics, thermodynamics, and quantum critical phenom ena in many-body physics, see a review.[3,4] In the context of ultracold atoms, the 1D Bose gas with a repulsive short-range interaction characterized by a tunable coupling constant ex hibits rich many-body properties. This model thus becomes an ideal test ground to explore fundamental many-body phe nomena ranging from equilibrium to nonequilibrium physics in the experiment.