Tuning the Critical Current in Toroidal Superfluids via Controllable Impurities

TL;DR

The study tackles how controllable impurities influence the stability of persistent currents in a toroidal Bose–Einstein condensate. By integrating 3D Gross–Pitaevskii simulations with precision experiments, it demonstrates that increasing impurity density $n$ raises the critical winding $w_c$, thereby stabilizing the current and enabling a vortex-emission–driven current switch at high impurity counts. In the unstable regime, dissipation and the final winding are governed by vortex–impurity interactions, with pinning and unpinning events setting the timescale, consistent with a Landau-like criterion based on the time-averaged local velocity $v_{max}$ relative to the bulk sound speed $c_{bulk}$. These results establish a tunable platform for exploring universal mechanisms of superflow stabilization and decay, with potential applications in atomtronic quantum technologies, provided that impurity configurations can be controlled with sufficient precision.

Abstract

We combine numerical and experimental approaches to study how impurities affect the maximum superflow in an annular Bose-Einstein condensate. By tuning the impurity density, we achieve precise control over the stability of persistent currents which increases with the impurity number. In the unstable regime, the complex vortex motion within the impurity landscape, characterized by pinning and unpinning events, governs the timescale of the current decay and its final value. Our work establishes atomic superfluids as a pristine platform for exploring universal mechanisms of superflow stabilization and decay, paving the way for atomtronic quantum technologies.

Figures (3)

• Figure 1: Phase diagram of a ring superfluid with symmetric impurities. (a) Snapshots of the density in the $x$-$y$ plane (integrated along the $z$ axis) at different times for the unstable dynamics with $n=8$ impurities and initial winding $w_0=6>w_c$: $t= 0 \,$ms (i), $5.7\,$ms (ii), $7.0\,$ms (iii), $8.9\,$ms (iv), $15.3\,$ms (v) and $20.3\,$ms (vi). (b) Average winding number $\langle w(t) \rangle$ as a function of time, for different values of $n$ and fixed $w_0=6$. The initial temporal evolution (for $t \lesssim 0.5\, T_{w_0}$) for $n=8$ corresponds to the snapshot shown in panel (a). Times are rescaled in rotation units notaunits. (c) Stability phase diagram of the persistent current as a function of $n$ and $w_0$ in terms of $\bar{v}_{\max}/\bar{c}_{\rm bulk}$ (see text). The dark gray dots indicate the critical winding number $w_c$, the solid line is a guide to the eye. (d) Time averaged superfluid velocity $\bar{v}_{\max}/\bar{c}_{\rm bulk}$ as a function of $n$ at fixed $w_0=5$ and for $n \geq 5$, corresponding to the stable configurations for the chosen $w_0$. The inset reports the angular velocity taken at fixed radius $R^*$ for $w_0$ = 5 and $n=12$.
• Figure 2: Role of impurity distribution on the current stability. (a) The two-dimensional condensate density in the $xy$-plane, initially [(i) and (iii)], and after the vortex emission [(ii) and (iv)]. The cases (i) and (ii) refer to $n=6$ impurities displaced at the ring edge, while in (iii) and (iv) only one impurity (highlighted by the white arrow) is shifted toward the inner edge, the other impurities being at mid-radius $\bar{r}$. (b) Critical winding number as a function of the radial position shift $\Delta r/\xi$ for $n=6$. Green (grey) dots show the case when all (one) impurities are shifted from $\bar{r}$. Lines are guide to the eye. Inset: Scaled superfluid velocity $\bar{v}_{\max}/\bar{c}_{\rm bulk}$ at fixed $w_0=4$ and $n=6$, in the symmetric configuration where all impurities are displaced by $\Delta r/\xi$. (d-e) The final winding number $w_f$ (d) and the decay time $\tau$ in rotation units notaunits(e) with corresponding error bars as extracted from an exponential fit of the current decay for different impurity shifts $\Delta r /\xi$ in the symmetric configuration. Here we plot the results for the first unstable winding for each impurity configuration, namely for initial winding $w_0 = w_c +1$.
• Figure 3: Experimental results for impurities arranged at the ring center (a) In situ images of the superfluid ring pierced by 6 (i) and 12 (ii) impurities of Gaussian shape with height $V_0/\mu = 3.7(7)$ and width $\sigma = 1.4(1) \, \mu$m (see Appendix \ref{['AppB']} for details). The central disk provides the phase reference for the interferometric probe of circulation. Each image corresponds to the average over $6$ independent realizations. (b) Measured circulation as a function of time in rotation units notaunits for $w_0=6$ and different number of impurities (see legend). Error bars here represent the standard deviation of the mean value over repeated realizations. The solid lines are exponential fit of the experimental data, from which we extract the decay time $\tau$. (c) Stability diagram for different initial circulation $w_0$ and number of impurities $n$. The color scale reports the relative circulation change $\Delta w/w_0 = (w_0-w_F)/w_F$, where $w_F$ is the average circulation measured at $t = 180 \,$ms. (d) Decay time $\tau$ extracted from the fit as in panel (b), as a function of the number of impurities for $w_0=6$. Circles are experimental results, whereas the blue shaded area is the results of numerical simulations taking into account fluctuations in the impurities positions, widths and heights. The dashed gray line marks the transition value at which the system turns from unstable to stable for identical impurity, i.e., of same height, width and center's position.