A spin-orbit-coupled two-dimensional Bose gas is shown to simultaneously possess quasi- and true long-range order in the total and relative phase sectors, respectively. The total phase undergoes a Berenzinskii-Kosterlitz-Thouless transition to a low-temperature phase with quasi-long-range order, as expected for a two-dimensional quantum gas. Additionally, the relative phase undergoes an Ising-type transition building up true long-range order, which is induced by the anisotropic spin-orbit coupling in combination with spin-dependent particle-particle interactions. Based on the Bogoliubov approach, expressions for the total- and relative-phase fluctuations are derived analytically for the low-temperature regime. Numerical simulations of the stochastic projected Gross-Pitaevskii equation give a good agreement with the analytical predictions.
All Science Journal Classification (ASJC) codes
- Atomic and Molecular Physics, and Optics