Dynamic Kosterlitz-Thouless theory for two-dimensional ultracold atomic gases

作     者：Zhigang Wu Shizhong Zhang Hui Zhai 

作者机构：Shenzhen Institute for Quantum Science and Engineering Southern University of Science and Technology Shenzhen 518055 Guangdong China Guangdong Provincial Key Laboratory of Quantum Science and Engineering Southern University of Science and Technology Shenzhen 518055 Guangdong China Department of Physics and HKU-UCAS Joint Institute for Theoretical and Computational Physics at Hong Kong University of Hong Kong Hong Kong China Institute for Advanced Study Tsinghua University Beijing 100084 China Center for Quantum Computing Peng Cheng Laboratory Shenzhen 518055 China 

出 版 物：《Physical Review A》 (Phys. Rev. A)

年 卷 期：2020年第102卷第4期

页      面：043311-043311页

核心收录：

基　　金：Beijing Distinguished Young Scientist Program Guangdong Provincial Key Laboratory, (17305218, 2019B121203002, C6005-17G, HK GRF 17318316) Croucher Foundation National Natural Science Foundation of China, NSFC, (11974161) Ministry of Science and Technology of the People's Republic of China, MOST, (11734010, 2016YFA0301600) Special Project for Research and Development in Key areas of Guangdong Province, (2019B030330001) 

主　　题：BKT transition Bose-Einstein condensates Cold atoms & matter waves Superfluidity Vortices in superfluids 

摘      要：In this paper we develop a theory for the first and second sounds in a two-dimensional atomic gas across the superfluid transition based on the dynamic Koterlitz-Thouless theory. We employ a set of modified two-fluid hydrodynamic equations which incorporate the dynamics of the quantized vortices, rather than the conventional ones for a three-dimensional superfluid. As far as the sound dispersion equation is concerned, the modification is essentially equivalent to replacing the static superfluid density with a frequency-dependent one, renormalized by the frequency-dependent “dielectric constant of the vortices. This theory has two direct consequences. First, because the renormalized superfluid density at finite frequencies does not display discontinuity across the superfluid transition, in contrast to the static superfluid density, the sound velocities vary smoothly across the transition. Second, the theory includes dissipation due to free vortices and thus naturally describes the sound-to-diffusion crossover for the second sound in the normal phase. With only one fitting parameter, our theory gives a perfect agreement with the experimental measurements of sound velocities across the transition, as well as the quality factor in the vicinity of the transition. The predictions from this theory can be further verified by future experiments.