Shaping Long-lived Electron Wavepackets for Customizable Optical Spectra

Abstract: 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.