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arXiv:2007.07777 · Physical Review A

Josephson effect with superfluid fermions in the two-dimensional BCS-BEC crossover

Filippo Pascucci, Luca Salasnich

Published Jul 29, 2020• 9 citations
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Abstract

We investigate the macroscopic quantum tunneling of fermionic superfluids in the two-dimensional BCS-BEC crossover by using an effective tunneling energy which explicitly depends on the condensate fraction and the chemical potential of the system. We compare the mean-field effective tunneling energy with the beyond-mean-field one, finding that the mean-field tunneling energy is not reliable in the BEC regime of the crossover. Then we solve the Josephson equations of the population imbalance and the relative phase, calculating the frequency of tunneling oscillation both in the linear regime and in the nonlinear one. Our results show that the Josephson frequency is higher in the intermediate regime of the BCS-BEC crossover due to the peculiar behavior of the effective tunneling energy in the crossover.

DOI
10.1103/physreva.102.013325

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We investigate the macroscopic quantum tunneling of fermionic superfluids in the two-dimensional BCS-BEC crossover by using an effective tunneling energy which explicitly depends on the condensate fraction and the chemical potential of the system. We compare the mean-field effective tunneling energy with the beyond-mean-field one, finding that the mean-field tunneling energy is not reliable in the BEC regime of the crossover. Then we solve the Josephson equations of the population imbalance and the relative phase, calculating the frequency of tunneling oscillation both in the linear regime and in the nonlinear one. Our results show that the Josephson frequency is higher in the intermediate regime of the BCS-BEC crossover due to the peculiar behavior of the effective tunneling energy in the crossover.
The Josephson effect is a macroscopic quantum phenomenon that reveals the broken symmetry associated with any superfluid state. Here we report on the observation of the Josephson effect between two fermionic superfluids coupled through a thin tunneling barrier. We show that the relative population and phase are canonically conjugate dynamical variables throughout the crossover from the molecular Bose-Einstein condensate (BEC) to the Bardeen-Cooper-Schrieffer (BCS) superfluid regime. For larger initial excitations from equilibrium, the dynamics of the superfluids become dissipative, which we ascribe to the propagation of vortices through the superfluid bulk. Our results highlight the robust nature of resonant superfluids.
We study the macroscopic quantum tunneling of two weakly linked superfluids made of interacting fermionic atoms. We derive atomic Josephson junction equations and find that zero-mode and $\ensuremath{\pi}$-mode frequencies of coherent atomic oscillations depend on the tunneling coefficient and the sound velocity of the superfluid. By considering a superfluid of 40K^{40}\text{K}40K atoms, we calculate these oscillation frequencies in the crossover from the Bardeen-Cooper-Schrieffer state of weakly bound Cooper pairs to the Bose-Einstein condensate of strongly bound molecular dimers.
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.
By considering the contribution of the higher-order term representing the lowest approximation of beyond mean field corrections, we investigate a superfluid Fermi gas confined in a double-well potential in Bose–Einstein Condensation (BEC) side of the Bardeen–Cooper–Schrieffer (BCS) to BEC crossover. Two limited cases of deep BEC regime and BEC regime of BCS–BEC crossover, corresponding to the two-body scattering length a sc is small enough and large enough, respectively. We derive a simple two-mode model that could depict the dynamics effectively. With making thorough analysis on the two-mode model and its corresponding classical Hamiltonian, we find that the Josephson oscillation or self-trapping phenomenon could emerge at certain parameters. We find three kinds of the phase states: Josephson oscillation (JO), oscillating-phase-type self-trapping (OPTST) and running-phase-type self-trapping (RPTST). The dependence of these three phase states on the dimensionless interaction parameter y = 1/(kFa sc ) and the initial system energy are given in this paper.