Optomechanics and quantum phase of the Bose-Einstein condensate with the cavity mediated spin-orbit coupling

We investigated the optomechanical dynamics and explored the quantum phase of a Bose-Einstein condensate in a ring cavity. The interaction between the atoms and the cavity field in the running wave mode induces a semiquantized spin-orbit coupling (SOC) for the atoms. We found that the evolution of the magnetic excitations of the matter field resembles that of an optomechanical oscillator moving in a viscous optical medium, with very good integrability and traceability, regardless of the atomic interaction. Moreover, the light-atom coupling induces a sign-changeable long-range interatomic interaction, which reshapes the typical energy spectrum of the system in a drastic manner. As a result, a new quantum phase featuring a high quantum degeneracy was found in the transitional area for SOC. Our scheme is immediately realizable and the results are measurable in experiments.(c) 2023 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement