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.
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