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

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, 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.

Figures (3)

• Figure 1: The DC Josephson current as a function of interaction strength (the black solid line) when the system changes from BCS to BEC regime. The tunneling is between two condensates with the same interaction strength, which is tuned from BCS to BEC limit. The momentum cutoff for the tunneling coupling strength is chosen to be $\Lambda=2k_{\rm F}$. $\mathcal{N}_1=9\mathcal{T}^2N^2\sin{(\Delta\phi)}/\epsilon_{\rm F}$ is the normalizing factor with $N=k^3_{\rm F}/(3\pi^2)$ denoting the number density. The blue dashed line shows the asymptotic behavior of the DC current in BCS limit. The inset figure shows the numerical result (black solid line) and the asymptotic analytical solution (red dashed line) of the DC current in deeper BEC limit, with $2<(ak_{\rm F})^{-1}<4$.
• Figure 2: The AC Josephson current with different interaction strengths in the right reservoir. The top left corner shows the values of interaction strength in the right side. $\mathcal{N}_2=9\mathcal{T}^2|\tilde{\Delta}_{\rm BCS}|N^2/(4\epsilon_{\rm F})$ is the normalizing factor. The initial phase bias is taken to be $\Delta\phi=0$ to minimize the Josephson energy. The periods of current are proportional to the reciprocal of chemical potential bias $1/\Delta\mu$. The time $t$ is normalized by the Fermi energy $\epsilon_{\rm F}$ in the left reservoir.
• Figure 3: The amplitude of AC Josephson current when the right side changes from BCS to BEC regime. The left reservoir is fixed in BCS limit and the right side is tune from BCS to BEC limit. A peak is found near $(ak_{\rm F})^{-1}\approx0.8$, corresponding to the Riedel peak.