  Electrons in atoms and molecules are versatile physical systems covering a
vast range of light-matter interactions, enabling the physics of Rydberg
states, photon-photon bound states, simulation of condensed matter
Hamiltonians, and quantum sources of light. A limitation on the versatility of
such electronic systems for optical interactions would appear to arise from the
discrete nature of the electronic transitions and from the limited ionization
energy, constraining the energy scale through which the rich physics of bound
electrons can be accessed. In this work, we propose the concept of shaping
spatially confined electron wavepackets as superpositions of extended states in
the ionization continuum. These wavepackets enable customizable optical
emission spectra transitions in the eV-keV range. We find that the specific
shaping lengthens the diffraction lifetime of the wavepackets in exchange for
increasing their spatial spreads. Finally, we study the spontaneous radiative
transitions of these excited states, examining the influence of the wavepacket
shape and size on the radiation rate of the excited state. We observe that the
rate of radiative capture is primarily limited by the diffraction lifetime of
the wavepacket. The approach proposed in this work could have applications
towards developing designer emitters at tunable energy and length scales,
potentially bringing the physics of Rydberg states to new energy scales and
extending the range and versatility of emitters that can be developed using
shaped electrons.
