  Although the concept of random close packing with an almost universal packing
fraction of ~ 0.64 for hard spheres was introduced more than half a century
ago, there are still ongoing debates. The main difficulty in searching the
densest packing is that states with packing fractions beyond the glass
transition at ~ 0.58 are inherently non-equilibrium systems, where the dynamics
slows down with a structural relaxation time diverging with density; hence, the
random close packing is inaccessible. Here we perform simulations of
self-propelled hard spheres, and we find that with increasing activity the
relaxation dynamics can be sped up by orders of magnitude. The glass transition
shifts to higher packing fractions upon increasing the activity, allowing the
study of sphere packings with fluid-like dynamics at packing fractions close to
random close packing. Our study opens new possibilities of investigating dense
packings and the glass transition in systems of hard particles.
