  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.
