  The spin-asymmetric Josephson effect is a proposed quantum-coherent
tunnelling phenomenon where Cooper-paired fermionic spin-$\frac{1}{2}$
particles, which are subjected to spin-dependent potentials across a Josephson
junction, undergo frequency-synchronized alternating-current Josephson
oscillations with spin-dependent amplitudes. Here, in line with present-day
techniques in ultracold Fermi gas setups, we consider the regime of small
Josephson oscillations and show that the Josephson plasma oscillation amplitude
becomes spin-dependent in the presence of spin-dependent potentials while the
Josephson plasma frequency is the same for both spin-components. Detecting
these spin-dependent Josephson plasma oscillations provides a possible means to
establish the yet-unobserved spin-asymmetric Josephson effect with ultracold
Fermi gases using existing experimental tools.
