Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Time-reversal-invariant spin-orbit-coupled bilayer Bose-Einstein
  Condensates   Time-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.

33
The categories of this paper are: plasm-ph
16
The categories of this paper are: stat
13
The categories of this paper are: quant-ph
11
The categories of this paper are: hep-lat
24
The categories of this paper are: dg-ga
19
The categories of this paper are: eess
10
The categories of this paper are: q-bio
32
The categories of this paper are: atom-ph
29
The categories of this paper are: funct-an
17
The categories of this paper are: q-fin
9
The categories of this paper are: nlin
5
The categories of this paper are: gr-qc
36
The categories of this paper are: cmp-lg
20
The categories of this paper are: acc-phys
14
The categories of this paper are: math-ph
2
The categories of this paper are: math