Electrons on Helium using circuit quantum electrodynamics[1]

It is possible to form a two dimensional electron gas at the interface between superfluid helium and vacuum.~ This unique heterostructure has exceptional bulk properties including electron mobilities exceeding 10$^{7}$ cm$^{2}$/Vs and electron spin coherence times estimated to exceed 100s.~ One of the first proposals [2] for quantum computation employed the \textit{vertical} motional states of electrons on helium but coherent interactions have yet to be realized.~ I will describe a new proposal [3] which uses a high finesse superconducting transmission line cavity to detect and manipulate the \textit{lateral} motional and spin states of a single trapped electron on helium. We estimate that it is possible to attain vacuum Rabi frequencies of g=10 MHz and T$_{1}\sim $T$_{2}\sim $1 ms for the motional state and perhaps even longer coherence times if spin encoding is used. \newline \newline [1] Wallraff, et. al. Nature, 2004, 431, 162 \newline [2] Plattzman and Dykman, Science, 1999, 284, 1967 \newline [3] In preparation