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arXiv:2604.00574 · Physical review. B./Physical review. B

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

Soma Takemori, Kazuki Yamamoto

cond-mat.quant-gascond-mat.stat-mechcond-mat.str-elcond-mat.supr-conquant-phSubmitted Apr 1, 2026• Announced Apr 2, 2026• 0 citations• Revised Aug 18, 2026 (v2)
v1 · Apr 1, 2026v2 · Aug 18, 2026
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Abstract

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 $V_{31}$ between superfluids without two-body loss is weak, a two-step nonequilibrium phase transition characterized by the vanishing dc Josephson currents occurs: dissipation first induces the nonequilibrium phase transition by making one dc Josephson current finite, while further increasing dissipation makes this remaining dc Josephson current vanish. By contrast, when $V_{31}$ is strong, dissipation induces the nonequilibrium phase transition in which all dc Josephson currents simultaneously vanish. An analytical study based on a simplified model further supports this observation.

Journal reference
Physical Review B 114, 084508 (2026)
DOI
10.1103/r9gx-gy1s
Comments
16 pages, 12 figures

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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 V31V_{31}V31​ between superfluids without two-body loss is weak, a two-step nonequilibrium phase transition characterized by the vanishing dc Josephson currents occurs: dissipation first induces the nonequilibrium phase transition by making one dc Josephson current finite, while further increasing dissipation makes this remaining dc Josephson current vanish. By contrast, when V31V_{31}V31​ is strong, dissipation induces the nonequilibrium phase transition in which all dc Josephson currents simultaneously vanish. An analytical study based on a simplified model further supports this observation.
We predict a new mechanism to induce collective excitations and a nonequilibrium phase transition of fermionic superfluids via a sudden switch on of two-body loss, for which we extend the BCS theory to fully incorporate a change in particle number. We find that a sudden switch on of dissipation induces an amplitude oscillation of the superfluid order parameter accompanied by a chirped phase rotation as a consequence of particle loss. We demonstrate that when dissipation is introduced to one of the two superfluids coupled via a Josephson junction, it gives rise to a nonequilibrium dynamical phase transition characterized by the vanishing dc Josephson current. The dissipation-induced collective modes and nonequilibrium phase transition can be realized with ultracold fermionic atoms subject to inelastic collisions.
We study the emergence of dissipation in an atomic Josephson junction between weakly coupled superfluid Fermi gases. We find that vortex-induced phase slippage is the dominant microscopic source of dissipation across the Bose-Einstein condensate-Bardeen-Cooper-Schrieffer crossover. We explore different dynamical regimes by tuning the bias chemical potential between the two superfluid reservoirs. For small excitations, we observe dissipation and phase coherence to coexist, with a resistive current followed by well-defined Josephson oscillations. We link the junction transport properties to the phase-slippage mechanism, finding that vortex nucleation is primarily responsible for the observed trends of conductance and critical current. For large excitations, we observe the irreversible loss of coherence between the two superfluids, and transport cannot be described only within an uncorrelated phase-slip picture. Our findings open new directions for investigating the interplay between dissipative and superfluid transport in strongly correlated Fermi systems, and general concepts in out-of-equilibrium quantum systems.
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© 2020 The Author(s). Published by IOP Publishing Ltd on behalf of the Institute of Physics and Deutsche Physikalische Gesellschaft.We provide a complete study of the phase diagram characterising the distinct dynamical regimes emerging in a three-dimensional Josephson junction in an ultracold quantum gas. Considering trapped ultracold superfluids separated into two reservoirs by a barrier of variable height and width, we analyse the population imbalance dynamics following a variable initial population mismatch. We demonstrate that as the chemical potential difference is increased, the system transitions from Josephson plasma oscillations to either a dissipative (in the limit of low and narrow barriers) or a self-trapped regime (for large and wider barriers), with a crossover between the dissipative and the self-trapping regimes which we explore and characterize for the first time. This work, which extends beyond the validity of the standard two-mode model, connects the role of the barrier width, vortex rings and associated acoustic emission with different regimes of the superfluid dynamics across the junction, establishing a framework for its experimental observation, which is found to be within current experimental reach.
Abstract We provide a complete study of the phase diagram characterising the distinct dynamical regimes emerging in a three-dimensional Josephson junction in an ultracold quantum gas. Considering trapped ultracold superfluids separated into two reservoirs by a barrier of variable height and width, we analyse the population imbalance dynamics following a variable initial population mismatch. We demonstrate that as the chemical potential difference is increased, the system transitions from Josephson plasma oscillations to either a dissipative (in the limit of low and narrow barriers) or a self-trapped regime (for large and wider barriers), with a crossover between the dissipative and the self-trapping regimes which we explore and characterize for the first time. This work, which extends beyond the validity of the standard two-mode model, connects the role of the barrier width, vortex rings and associated acoustic emission with different regimes of the superfluid dynamics across the junction, establishing a framework for its experimental observation, which is found to be within current experimental reach.
The direct-current (dc) Josephson effect provides a phase-sensitive tool for investigating superfluid order parameters. We report on the observation of dc Josephson supercurrents in strongly interacting fermionic superfluids across a tunneling barrier in the absence of any applied potential difference. For sufficiently strong barriers, we observed a sinusoidal current-phase relation, in agreement with Josephson's seminal prediction. We mapped out the zero-resistance state and its breakdown as a function of junction parameters, extracting the Josephson critical current behavior. By comparing our results with an analytic model, we determined the pair condensate fraction throughout the Bardeen-Cooper-Schrieffer-Bose-Einstein condensation crossover. Our work suggests that coherent Josephson transport may be used to pin down superfluid order parameters in diverse atomic systems, even in the presence of strong correlations.