Electrons on helium form a unique two-dimensional system on the interface of superfluid $^4$He and vacuum. At low temperatures and weak confinement, trapped electrons can arrange into strongly correlated states known as Wigner molecules, which can be used to study electron interactions in the absence of disorder, or as a promising resource for quantum computation. Wigner molecules have orbital frequencies in the microwave regime and can therefore be integrated with circuit quantum electrodynamics, which would allow rapid detection and manipulation of such a molecule's orbital state. In this thesis, we demonstrate deterministic preparation of one to four-electron Wigner molecules in an electron-on-helium quantum dot located at the tip of an on-chip microwave resonator. The Wigner molecule dipole coupling to the resonator allows us to measure spectral features of Wigner molecules in the microwave regime. We find that different-sized Wigner molecules have strikingly different spectra, and each spectrum serves as a fingerprint for the molecule's internal structure and its surroundings. By modeling the electron-cavity system, we extract each molecule's orbital frequency and electron configuration. For a single electron, the orbital frequency crosses the cavity resonance and we measure a large coherent electron-photon coupling rate of $g/2\pi = 4.8$ MHz, which exceeds the incoherent cavity decay rate by ten times. These results provide a solid base for the development of an electron-on-helium qubit. Looking forward, our platform allows for new microwave studies of strongly correlated electron states and can be used to couple a single microwave photon to a single electron spin.




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