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arXiv:2603.25577 · Physical review. B./Physical review. B

Josephson effects in an interaction-asymmetric junction across the BCS-BEC crossover

Anonymous, Hiroyuki Tajima

Published Jul 22, 2026• 0 citations
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Abstract

We theoretically study the Josephson effect in ultracold Fermi gases, where the two sides of the Josephson junction are independently tuned to different regions of the Bardeen-Cooper-Schrieffer (BCS)-Bose-Einstein condensation (BEC) crossover. Using the nonequilibrium Green's function approach combined with the tunnel Hamiltonian formalism and a mean-field approach, we evaluate the DC and AC Josephson currents throughout the entire crossover region. We calculate the DC Josephson current as a function of interaction strength by tuning both sides of the junction synchronously from the BCS to the BEC regimes, and give the asymptotic expression of the current in the deep BCS and BEC limits. We also study the AC Josephson junction through the interaction-asymmetric junction by fixing the interaction in one reservoir and tuning that of the other one. A peak of the tunneling current is found when one side is fixed in the BCS limit and the other side is tuned into the BEC regime, which corresponds to the interaction-biased Riedel peak. Our results indicate the competition between contributions of increasing pair spectral weight and decreasing chemical potential to Josephson tunneling throughout the BCS-BEC crossover, and demonstrate the realization of the Riedel peak in strong-coupling quantum gases.

DOI
10.1103/2dfl-p433

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We theoretically study the Josephson effect in ultracold Fermi gases, where the two sides of the Josephson junction are independently tuned to different regions of the Bardeen-Cooper-Schrieffer (BCS)-Bose-Einstein condensation (BEC) crossover. Using the nonequilibrium Green's function approach combined with the tunnel Hamiltonian formalism and a mean-field approach, we evaluate the DC and AC Josephson currents throughout the entire crossover region. We calculate the DC Josephson current as a function of interaction strength by tuning both sides of the junction synchronously from the BCS to the BEC regimes, and give the asymptotic expression of the current in the deep BCS and BEC limits. We also study the AC Josephson junction through the interaction-asymmetric junction by fixing the interaction in one reservoir and tuning that of the other one. A peak of the tunneling current is found when one side is fixed in the BCS limit and the other side is tuned into the BEC regime, which corresponds to the interaction-biased Riedel peak. Our results indicate the competition between contributions of increasing pair spectral weight and decreasing chemical potential to Josephson tunneling throughout the BCS-BEC crossover, and demonstrate the realization of the Riedel peak in strong-coupling quantum gases.
We develop a microscopic model to describe the Josephson tunneling between two superfluid reservoirs of ultracold fermionic atoms which accounts for the dependence of the critical current on both the barrier height and the interaction strength along the crossover from the BCS to the BEC regime. Building on a previous study [F. Meier and W. Zwerger, Phys. Rev. A 64, 033610 (2001)] of weakly interacting bosons, we derive analytic results for the Josephson critical current at zero temperature for homogeneous and trapped systems at arbitrary coupling. The critical current exhibits a maximum near the unitarity limit which arises from the competition between the increasing condensate fraction and a decrease in the chemical potential along the evolution from the BCS to the BEC limit. Our results agree quantitatively with numerical simulations and recent experimental data.
We investigate the transport properties of a superfluid Fermi gas confined in a ring trap with a moving potential barrier across the Bardeen-Cooper-Schrieffer (BCS) to Bose-Einstein condensate (BEC) crossover. Employing time-dependent Bogoliubov--de Gennes (BdG) equations, we simulate the dynamics of a Josephson junction biased by both DC and AC currents. Over a wide range of interaction strengths, the barrier-velocity dependence of the chemical potential difference exhibits low-order plateau structures, consistent with Shapiro steps, with fitted levels close to integer multiples of ℏω/2\hbarω/2ℏω/2 within the phase-coherent regime. This factor of 1/21/21/2 reflects our convention of defining the chemical potential per single fermion in the BdG framework. Microscopic analysis reveals that these fundamental steps originate from synchronized phase slips mediated by periodic soliton generation at the barrier. Our findings clarify the role of interaction regimes in the nonequilibrium phase dynamics of ring-trapped fermionic superfluids and provide microscopic insights relevant to future studies of atomtronic systems with nontrivial topology.
Transport in Josephson junctions is commonly described using a simplifying assumption called the Andreev approximation, which assumes that excitations are fixed at the Fermi momentum and only Andreev reflections occur at interfaces (with no normal reflections). This approximation is appropriate for BCS-type superconductors, where the chemical potential vastly exceeds the pairing gap, but it breaks down for superconductors with low carrier density, such as topological superconductors, doped semiconductors, or superfluid quantum gases. Here, we present a generic analyticalanalyticalanalytical framework for calculating transport in Josephson junctions that lifts up the requirement of the Andreev approximation. Using this general framework, we study in detail transport in Josephson junctions across the BCS-BEC crossover, which describes the evolution from a BCS-type superconductor with loosely-paired Cooper pairs to a BEC of tighly-paired dimers. As the interaction is tuned from the BCS to the BEC regime, we find that the overall subgap current caused by multiple Andreev reflections decreases, but nonlinearities in the current-voltage characteristic called the subharmonic gap structure become more pronounced near the intermediate unitary limit, giving rise to sharp peaks and dips in the differential conductance with even negativenegativenegative conductance at specific voltages.
A gas of interacting ultracold fermions can be tuned into a strongly interacting regime using a Feshbach resonance. Here, we theoretically study quasiparticle transport in a system of two reservoirs of interacting ultracold fermions on the BCS side of the BCS-BEC crossover coupled weakly via a tunnel junction. Using the generalized BCS theory, we calculate the time evolution of the system that is assumed to be initially prepared in a nonequilibrium state characterized by a particle number imbalance or a temperature imbalance. A number of characteristic features like sharp peaks in quasiparticle currents or transitions between the normal and superconducting states are found. We discuss signatures of the Seebeck and the Peltier effects and the resulting temperature difference of the two reservoirs as a function of the interaction parameter ${({k}_{F}a)}^{\ensuremath{-}1}$. The Peltier effect may lead to an additional cooling mechanism for ultracold fermionic atoms.
Abstract We present a theoretical review of the recent progress in non-equilibrium BCS (Bardeen-Cooper-Schrieffer)-BEC (Bose-Einstein condensation) crossover physics. As a paradigmatic example, we consider a strongly interacting driven-dissipative two-component Fermi gas where the non-equilibrium steady state is tuned by adjusting the chemical potential difference between two reservoirs that are coupled with the system. As a powerful theoretical tool to deal with this system, we employ the Schwinger-Keldysh Green’s function technique. We systematically evaluate the superfluid transition, as well as the single-particle properties, in the non-equilibrium BCS-BEC crossover region, by adjusting the chemical potential difference between the reservoirs and the strength of an s-wave pairing interaction associated with a Feshbach resonance. In the weak-coupling BCS side, the chemical potential difference is shown to imprint a two-step structure on the particle momentum distribution, leading to an anomalous enhancement of pseudogap, as well as the emergence of exotic Fulde-Ferrell-Larkin-Ovchinnikov-type superfluid instability. Since various non-equilibrium situations have recently been realized in ultracold Fermi gases, the theoretical understanding of non-equilibrium BCS-BEC crossover physics would become increasingly important in this research field.