supported by the Chinese Academy of Sciences Strategic Priority Research Program(XDB35020100);the National Key Research and Development Program of China(2021YFA1400900 and 2018YFA0305601);the National Natural Science Foundation of China(11874073,12304564,11825401,12204187,12261160368);the Open Project of Shenzhen Institute of Quantum Science and Engineering(SIQSE202003);the Hefei National Laboratory;the Scientific and Technological Innovation 2030 Key Program of Quantum Communication and Quantum Computing(2021ZD0301903 and 2021ZD0302000)。
The realization of spin-orbit-coupled ultracold gases has driven a wide range of research and is typically based on the rotating wave approximation(RWA).By neglecting the counter-rotating terms,RWA characterizes a sin...