Connecting Dissipation and Phase Slips in a Josephson Junction between Fermionic Superfluids

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.

Figure 1

(a) In situ density profile of an atomic superfluid bisected by a thin barrier with $z_0\simeq 0.23$. (b) Sketch of a phase-slip event: a vortex ring is created within the junction at time $t$, and it subsequently penetrates into the superfluid bulk after shrinking. (c),(d) Typical population imbalance $z$ and relative phase $\phi$ evolutions for a molecular BEC at $1/(k_{F}a)=4.6$ and $V_0/\mu =0.7$. Both solid curves are obtained by a single fit of the measured $z(t)$ with the solution of a RSJ-like circuit model (see text). Error bars in panel (c) denote standard errors over at least five independent measurements, while light (dark) circles in panel (d) represent single (averaged) experimental realizations. (e) Standard deviation of the measured $\phi$. The two peaks at short times are associated with stochastic phase-slip events, where shot-to-shot fluctuations are maximized.

Figure 2

(a)–(c) Evolution of the relative population imbalance with $z_0\simeq 0.2$ for (a) a molecular BEC at $V_0/\mu \simeq 1$, (b) a unitary Fermi gas at $V_0/\mu \simeq 0.9$, and (c) a BCS superfluid at $V_0/\mu \simeq 0.9$. Solid lines are fitted to the data with the solution of the circuital model described in the text. Error bars denote standard errors over at least five measurements. (d)–(f) Evolution of average vortex counts $⟨N_v⟩$ for the same experimental conditions as in panels (a)–(c). The error bars are estimated as $\sqrt{{\sigma }_{Nv}^2+1/Z}$, with ${\sigma }_{Nv}$ the standard deviation of the mean and $Z$ the number of experimental measurements. The insets (i)–(iii) show typical time-of-flight images after 20 ms of evolution, where vortex defects are clearly visible. Residual images are also displayed, obtained by subtracting the density distribution of a cloud without excitations.

Figure 3

(a) Conductance $G$ and (b) critical current $I_c$ as a function of the central pair-density $n_0$ inside the barrier for BEC (blue circles), unitary (green squares), and BCS (red triangles) superfluids. For filled (empty) symbols, $G$ is obtained through the RSJ-like ($RC$) circuit model (see text). The dashed lines in panel (b) represent the calculated upper bound $I_{c0}$ [30], shown for comparison for BEC (blue) and unitary (green) superfluids. In both panels, horizontal error bars account for the typical 20% uncertainty on atom number, while vertical ones combine this with fitting standard errors.

Figure 4

(a)–(c) Crossover from Josephson to purely dissipative dynamics in a unitary superfluid at $V_0/\mu \simeq 0.9$. The initial bias potentials $\mathrm{\Delta }{\mu }_0/\mu$ are (a) 0.02, (b) 0.10, and (c) 0.39. (d) Average vortex counts $⟨N_v⟩$ and (e) conductance $G$ as a function of $\mathrm{\Delta }{\mu }_0/\mu$ for BEC superfluids at $V_0/\mu \simeq 1.3$ (blue circles) and unitary superfluids at $V_0/\mu \simeq 0.9$ (green squares). The central density $n_0$ is about 3 times larger for BECs with respect to unitary gases. The green shaded region indicates the range of $\mathrm{\Delta }{\mu }_0/\mu$ where $I_c>0$ at unitarity. Vertical error bars are computed as described in the caption of Figs. 2 and 3, while horizontal ones result from the experimental uncertainty on $z_0$, which is typically of $\pm 2\%$. Inset: time-of-flight image of an expanding unitary superfluid for $\mathrm{\Delta }{\mu }_0/\mu \simeq 0.35$, where several vortex defects are visible.