Abstract:
The correlation function is an important quantity in the physics of ultracold quantum gases because it
provides information about the quantum many-body wave function beyond the simple density
profile. In this paper we first study the M-body local correlation functions, gM, of the one-dimensional
(1D)strongly repulsive Bose gas within the Lieb–Liniger model using the analytical method proposed
by Gangardt and Shlyapnikov (2003 Phys. Rev. Lett. 90 010401; 2003 New J. Phys. 5 79). In the strong
repulsion regime the 1D Bose gas at low temperatures is equivalent to a gas of ideal particles obeying
the non-mutual generalized exclusion statistics with a statistical parameter a g = -1 2 , i.e. the
quasimomenta of N strongly interacting bosons map to the momenta of N free fermions via ki » aki
F
with i = ¼1, ,N. Here γ is the dimensionless interaction strength within the Lieb–Liniger model. We
rigorously prove that such a statistical parameter α solely determines the sub-leading order
contribution to the M-body local correlation function of the gas at strong but finite interaction
strengths. We explicitly calculate the correlation functions gM in terms of γ and α at zero, low, and
intermediate temperatures. For M = 2 and 3 our results reproduce the known expressions for g2 and g3
with sub-leading terms(see for instance (Vadim et al 2006 Phys. Rev. A 73 051604(R); Kormoset al
2009 Phys. Rev. Lett. 103 210404; Wang et al 2013 Phys. Rev. A 87 043634). We also express the leading
order of the short distance non-local correlation functions () ( ) ( ) () áY YY Y † † x xy y 1 M M ñ 1 of the
strongly repulsive Bose gas in terms of the wave function of M bosons at zero collision energy and zero
total momentum. Here Y(x)is the boson annihilation operator. These general formulas of the higher-order local and non-local correlation functions of the 1D Bose gas provide new insights into the many-body