Many-body phases of a planar Bose-Einstein condensate with cavity-induced spin-orbit coupling

We explore the many-body phases of a two-dimensional Bose-Einstein condensate with cavity-mediated dynamic spin-orbit coupling. With the help of two transverse noninterfering, counterpropagating pump lasers and a single standing-wave cavity mode, two degenerate Zeeman sub-levels of the quantum gas are Raman coupled in a double-A-configuration. Beyond a critical pump strength the cavity mode is populated via coherent superradiant Raman scattering from the two pump lasers, leading to the appearance of a dynamical spin-orbit coupling for the atoms. We identify three quantum phases with distinct atomic and photonic properties: the normal homogeneous phase, the superradiant spin-helix phase, and the superradiant supersolid spin-density-wave phase. The last exhibits an emergent periodic atomic density distribution with an orthorhombic centered rectangular-lattice structure due to the interplay between the coherent photon scattering into the resonator and the collision-induced momentum coupling. The transverse lattice spacing of the emergent crystal is set by the dynamic spin-orbit coupling.

Automated summary

In this study, we investigate the many-body phases of a two-dimensional Bose-Einstein condensate with cavity-mediated dynamic spin-orbit coupling. We identify three quantum phases with distinct atomic and photonic properties: the normal homogeneous phase, the superradiant spin-helix phase, and the superradiant supersolid spin-density-wave phase. The last phase exhibits an emergent crystal with a specific lattice structure in the atomic density distribution.