Macroscopic periodic tunneling of Fermi atoms in the BCS-BEC crossover

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 $\pi$-mode frequencies of coherent atomic oscillations depend on the tunneling coefficient and the sound velocity of the superfluid. By considering a superfluid of ${}^{40}\text{K}$ 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.

Figure 1

(Color online). Zero-mode frequency ${\nu }_0$ (solid) and $\pi$-mode frequency ${\nu }_{\pi }$ (dashed) for a superfluid of $N={10}^6$ ${}^{40}\text{K}$ atoms between two symmetric regions of volume $25\times {10}^6\mu {\text{m}}^3$ (mean density $n=0.02\mu {\text{m}}^{-3}$) and fixed tunneling parameter $K/k_{\text{B}}={10}^{-9}\text{K}$.

Figure 2

(Color online). Nonlinear effects on the zero-mode oscillation of $N={10}^6$ ${}^{40}\text{K}$ atoms between two symmetric regions with the same conditions of Fig. 1 at fixed interaction $a_F=1\mu \text{m}$, corresponding to $y=1.19$. These trajectories result from the integration of the coupled Eqs. (19, 20) for $z\left(t\right)$ (solid) and $\phi \left(t\right)$ (dashed), with initial conditions $\phi \left(0\right)=0$, and $z\left(0\right)=0.5$ (left) or $z\left(0\right)=0.999$ (right).

Figure 3

(Color online). Nonlinear effects on the zero-mode (solid) and $\pi$-mode (dashed) frequency (left) and waveform (right) for the same conditions as in Fig. 2, as functions of the initial amplitude $z\left(0\right)$. In an expansion $\phi \left(t\right)=\phi \left(0\right)+{\sum }_{k=1}^{\infty }{a}_k\text{sin}\left(2\pi \nu kt\right)$, the fractional leading Fourier component of the right panel is $a_1^2/{\sum }_k{a}_k^2$.