Modeling Strongly Interacting Electrons on Helium Coupled to a Microwave Resonator

Electrons on helium is a unique two-dimensional electron gas system formed at the interface of a quantum liquid (superfluid helium) and vacuum. If single electrons on helium can be isolated, the motional and spin states could form the building blocks for hybrid quantum computing [1,2]. However, to trap single electrons we must start from a 2-dimensional gas of many electrons, which is a strongly interacting classical gas. In our experiment, we trap mesoscopic samples of electrons in a micron-sized trap at the end of a centimeter-long quarter wavelength microwave cavity, and interrogate the system via the change in the microwave resonance frequency. Here, we will present a simple numeric model that we developed to understand the coupled cavity-electron on helium system in a micron-sized trap, and insights towards building a single electron quantum dot. [1] S. Lyon, Phys. Rev. A. 74, 5 (2006) [2] D.I. Schuster, et al. Phys. Rev. Lett. 105, 040503 (2010)