Increasing the stability of a superfluid in a rotating necklace potential

Recent experiments have probed the stability of ring superfluids in the presence of Josephson barriers or Gaussian impurities. Here we present a theoretical analysis that extends beyond the regimes explored so far. We study the onset of dynamical instabilities in a ring superfluid, addressing both tunneling and hydrodynamic regimes. The stability of the system is controlled by the effective rotation frequency $ω$, given by the difference between the initial quantized circulation and the frequency of barrier rotation. The instability occurs when $ω$ overcomes a critical value $ω_c$. We show that $ω_c$ increases approximately linearly with the number of barriers, with a slope set by the barrier height and width. When the system is quenched into the dynamically unstable regime, it emits multiple solitons, which can switch or even reverse the direction of circulation. The stabilization mechanism is robust against imperfections of the potential and does not require a perfectly periodic array of barriers. In particular, we find that adding a disordered speckle potential to an ordered array of barriers can further increase $ω_c$: disorder can therefore make a ring superfluid more resilient to dynamical instabilities.