Nonequilibrium phase transition of dissipative fermionic superfluids: Case study of multi-terminal Josephson junctions

We investigate nonequilibrium dynamics of a triad of fermionic superfluids connected via Josephson junctions, following sudden switch-on of two-body loss in one of the three superfluids. By formulating the dissipative BCS theory for the Lindblad equation, we find that the superfluid order parameter exhibits a phase rotation, thereby giving rise to three types of dc Josephson currents corresponding to different junctions. We demonstrate that, when the tunneling amplitude V₃₁ between superfluids without two-body loss is weak, two-step nonequilibrium dynamical phase transition (NDPT) characterized by the vanishing dc Josephson currents occurs: dissipation first induces the NDPT by making one dc Josephson current finite, while further increasing dissipation makes this remaining dc Josephson current vanish. By contrast, when V₃₁ is strong, dissipation induces the NDPT in which all dc Josephson currents simultaneously vanish. An analytical study based on a simplified model further supports this observation.