  The advent of bottom-up atomic manipulation heralded a new horizon for
attainable information density, as it allowed a bit of information to be
represented by a single atom. The discrete spacing between atoms in condensed
matter has thus set a rigid limit on the maximum possible information density.
While modern technologies are still far from this scale, all theoretical
downscaling of devices terminates at this spatial limit. Here, however, we
break this barrier with electronic quantum encoding scaled to subatomic
densities. We use atomic manipulation to first construct open
nanostructures--"molecular holograms"--which in turn concentrate information
into a medium free of lattice constraints: the quantum states of a
two-dimensional degenerate Fermi gas of electrons. The information embedded in
the holograms is transcoded at even smaller length scales into an atomically
uniform area of a copper surface, where it is densely projected into both two
spatial degrees of freedom and a third holographic dimension mapped to energy.
In analogy to optical volume holography, this requires precise amplitude and
phase engineering of electron wavefunctions to assemble pages of information
volumetrically. This data is read out by mapping the energy-resolved electron
density of states with a scanning tunnelling microscope. As the projection and
readout are both extremely near-field, and because we use native quantum states
rather than an external beam, we are not limited by lensing or collimation and
can create electronically projected objects with features as small as ~0.3 nm.
These techniques reach unprecedented densities exceeding 20 bits/nm2 and place
tens of bits into a single fermionic state.
