Maisberger, MatthewWang, Lin-ChengSun, KueiXu, YongZhang, Chuanwei2019-08-302019-08-302018-05-292469-9926https://hdl.handle.net/10735.1/6814Time-reversal invariance plays a crucial role for many exotic quantum phases, particularly for topologically nontrivial states, in spin-orbit coupled electronic systems. Recently realized spin-orbit coupled cold-atom systems, however, lack the time-reversal symmetry due to the inevitable presence of an effective transverse Zeeman field. We address this issue by analyzing a realistic scheme to preserve time-reversal symmetry in spin-orbit-coupled ultracold atoms, with the use of Hermite-Gaussian-laser-induced Raman transitions that preserve spin-layer time-reversal symmetry. We find that the system's quantum states form Kramers pairs, resulting in symmetry-protected gap closing of the lowest two bands at arbitrarily large Raman coupling. We also show that Bose gases in this setup exhibit interaction-induced layer-stripe and uniform phases as well as intriguing spin-layer symmetry and spin-layer correlation. © 2018 American Physical Society.en©2018 American Physical SocietyBose-Einstein condensationStatistical mechanicsElectronic systemsTime reversalQuantum theoryarticleMaisberger, M., L. -C Wang, K. Sun, Y. Xu, et al. 2018. "Time-reversal-invariant spin-orbit-coupled bilayer Bose-Einstein condensates." Physical Review A 97(5).975