Observation of Quantum Criticality and Luttinger Liquid in   One-dimensional Bose Gases
  We experimentally investigate the quantum criticality and Tomonaga-Luttinger liquid (TLL) behavior within one-dimensional (1D) ultracold atomic gases. Based on the measured density profiles at different temperatures, the universal scaling laws of thermodynamic quantities are observed. The quantum critical regime and the relevant crossover temperatures are determined through the double-peak structure of the specific heat. In the TLL regime, we obtain the Luttinger parameter by probing sound propagation. Furthermore, a characteristic power-law behavior emerges in the measured momentum distributions of the 1D ultracold gas, confirming the existence of the TLL. 
Bing Yang, Yang-Yang Chen, Yong-Guang Zheng, Hui Sun, Han-Ning Dai,   Xi-Wen Guan, Zhen-Sheng Yuan, Jian-Wei Pan
cond-mat.quant-gas