  The ideal glass, a disordered system of particles with zero configurational
entropy, cannot be realized through thermal processes. Nevertheless, we present
a method for constructing ideal jammed packings of soft spheres, and thus the
zero temperature ideal glass, in two dimensions. In line with the predicted
properties, these critically jammed packings have high bulk and shear moduli as
well as an anomalously high density. While the absence of pressure scaling in
the shear moduli of crystalline materials is often attributed to the ordered
nature of the particles, we show for the first time that disordered ideal
packings also have this feature. We also find that the density of states avoids
the low frequency power law scaling famously found in most amorphous materials.
Finally, these configurations display hyperuniformity. In addition to resolving
a long-standing mystery, this methodology represents a valuable shortcut in the
generation of well-equilibrated glassy systems. The creation of such an ideal
packing makes possible a complete exploration and explanation of two
dimensional jammed and glassy systems.
