  The higher the energy of a particle is above equilibrium the faster it
relaxes due to the growing phase-space of available electronic states it can
interact with. In the relaxation process phase coherence is lost, thus limiting
high energy quantum control and manipulation. In one-dimensional systems high
relaxation rates are expected to destabilize electronic quasiparticles. We show
here that the decoherence induced by relaxation of hot electrons in
one-dimensional semiconducting nanowires evolves non-monotonically with energy
such that above a certain threshold hot-electrons regain stability with
increasing energy. We directly observe this phenomenon by visualizing for the
first time the interference patterns of the quasi-one-dimensional electrons
using scanning tunneling microscopy. We visualize both the phase coherence
length of the one-dimensional electrons, as well as their phase coherence time,
captured by crystallographic Fabry-Perot resonators. A remarkable agreement
with a theoretical model reveals that the non-monotonic behavior is driven by
the unique manner in which one dimensional hot-electrons interact with the cold
electrons occupying the Fermi-sea. This newly discovered relaxation profile
suggests a high-energy regime for operating quantum applications that
necessitate extended coherence or long thermalization times, and may stabilize
electronic quasiparticles in one dimension.
