Ultrastable jammed sphere packings with a wide range of particle dispersities

We show that for a standard continuously-polydisperse model with particle-diameter distribution $P(\sigma) \propto \sigma^{-3}$ and polydispersity index $\Delta$, employing a combination of standard SWAP moves and transient degree of freedom (TDOF) moves during a Lubachevsky-Stillinger-like particle-growth process dramatically increases the generated packings' jamming densities $\phi_{\rm J}(\Delta)$ and coordination numbers $Z_{\rm J}(\Delta)$, for a wide range of $\Delta$. The fractional increase in $\phi_{\rm J}(\Delta)$ obtained by employing these moves first increases rapidly with $\Delta$, then plateaus at $6-7\%$ over the range $0.10 \lesssim \Delta \leq 50$; the obtained $\phi_{\rm J}$ are as high as $0.747$ (for $\Delta = 0.50$). These density increases are achieved without producing clearly-noticeable crystallization or increased fractionation, despite the fact that the packings are quite hyperstatic for all $\Delta > 0$. SWAP and TDOF moves also reduce packings' rattler populations by as much as 99% and increase their bulk moduli by as much as 80%.