  Atomically engineered artificial lattices are a useful tool for simulating
complex quantum phenomena, but have so far been limited to the study of
Hamiltonians where electron-electron interactions do not play a role -- but
it's precisely the regime in which these interactions do matter where
computational times lend simulations a critical advantage over numerical
methods. Here, we propose a new platform for constructing artificial matter
that relies on the confinement of field-emission resonances, a class of
vacuum-localized discretized electronic states. We use atom manipulation of
surface vacancies in a chlorine-terminated Cu(100) surface to reveal square
patches of the underlying metal, thereby creating atomically-precise potential
wells that host particle-in-a-box modes. By adjusting the shape and size of the
confining potential, we can access states with different quantum numbers,
making these patches attractive candidates as quantum dots or artificial atoms.
We demonstrate that the lifetime of electrons in these engineered states can be
extended and tuned through modification of the confining potential, either via
atomic assembly or by changing the tip-sample distance. We also demonstrate
control over a finite range of state-filling, a parameter which plays a key
role in the evolution of quantum many-body states. We model the transport
through the localized state to disentangle and quantify the lifetime-limiting
processes, illustrating the critical dependency of the electron lifetime on the
properties of the underlying bulk band structure. The interplay with the bulk
bands also gives rise to negative differential resistance, opening possible
avenues for engineering custom atomic-scale resonant tunnelling diodes, which
exhibit similar current-voltage characteristics.
