Quantum vortex channels as Josephson junctions

Abstract

In quantum gases, weak links are typically realized with externally imposed optical potentials. We show that, in rotating binary condensates, quantized vortices in one component form hollow channels that act as self-induced weak links for the other, enabling superflow through otherwise impenetrable, phase-separated domains. This introduces a novel barrier mechanism: quantum pressure creates an effective barrier inside the vortex channel, set by the constriction width, which controls the superflow. Tuning the interspecies interaction strength drives a crossover from the hydrodynamic transport to Josephson tunneling regime. Long-range dipolar interactions further tune the weak-link properties, enabling both short links and two coupled junctions in series. Circuit models quantitatively capture the dc current-phase relations for both configurations. These results establish vortices as reconfigurable, interaction-controlled Josephson elements in superfluids.

Figures (6)

• Figure 1: Vortex-mediated weak link. (a,b) Vortex-free immiscible state: component 1 (red, dipolar) blocks current in component 2 (blue, nondipolar). (c,d) A vortex oriented along $z$ resides in component 1; component 2 flows through its hollow core, carrying current $I_2$. Magnetostriction produces thin dipolar domains, yielding a short weak link Kirkby2023Spin. Density isosurfaces of comp. 1 (comp. 2) are shown at 45% (70%) of their respective peak densities. (d, lower): circuit model: an inductor in series with a nonlinear Josephson junction (cross), with total phase drop $\Delta\phi^{\mathrm{tot}}_{2}$ and junction phase drop $\Delta\phi^{\rm{J}}_{2}$. Parameters: interspecies scattering length $a_{12}=125\,a_0$; populations $N_2=4N_1=7.5\times 10^3$.
• Figure 2: Short vortex junction. (a) CPRs for different $a_{12}$ (barrier heights). Markers represent numerical data and dashed lines are the circuit model. Each CPR is normalized to its critical (peak) current $I_{c,2}$. Inset shows the corresponding core densities normalized to their peaks. (b) Effective potential inside the vortex core. (c) Vortex channel width $w$ (black) and barrier height $V_{b,2}$ (gray) versus interspecies scattering length.
• Figure 3: Long-vortex junction for three barrier strengths: (a) $a_{12}=220\,a_0$ (tunneling regime), (b) $a_{12}=150\,a_0$, and (c) $a_{12}=130\,a_0$ (hydrodynamic regime). (a2), (b), and (c2): CPRs with numerical data (markers) shown together with the simple circuit model [Eqs. \ref{['Eq:ModelPhase']}-\ref{['L_kin']}] (dashed lines) and the extended circuit model [Eq. \ref{['Eq:extendedmodel']}] (solid lines). (b, inset) depicts the effective barrier for all three values of $a_{12}$. (a1) shows a channel in the tunneling regime, whereas (c1) shows that in the hydrodynamic regime the dipolar interactions restructure the vortex core environment into a double junction: the flowing component (red) exhibits a density minimum near each end of the vortex separated by a density bulge in the middle. The first component is shown at 10% of its peak density and the second at 70%. (c3) Extended circuit model (top) and axial density (bottom). The local density maximum at the center of the vortex core is modeled by an additional kinetic inductance $L_1^{v}$, while the two minima are represented as Josephson elements.
• Figure 4: Protocol for imposing a linear phase gradient along the vortex-free component in a binary BEC. Imaginary time is then used to relax the phase profile to a DC stationary state.
• Figure 5: CPRs for (a) the short vortex and (b) the long vortex, plotted as a function of the phase difference $\Delta\phi_i^V$ restricted to the vortex core region. The inset in (a) illustrates the localized phase drop across the junction.