An oscillating Casimir potential between two impurities in a spin-orbit coupled Bose-Einstein condensate

We study the Casimir potential between two impurities immersed in a spin-orbit coupled BoseEinstein condensate (BEC) with plane-wave order. We find that, by exchanging the virtual phonons/excitations, a remarkable anisotropic oscillating potential with both positive and negative parts can be induced between the impurities, with the period of the oscillation depending on the spin-orbit coupling strength. As a consequence, this would inevitably lead to a non-central Casimir force, which can be tuned by varying the strength of spin-orbit coupling . These results are elucidated for BECs with one-dimensional Raman-induced and two-dimensional Rashba-type SOC.