  The quantized lateral motional states and the spin states of electrons
trapped on the surface of superfluid helium have been proposed as basic
building blocks of a scalable quantum computer. Circuit quantum electrodynamics
(cQED) allows strong dipole coupling between electrons and a high-Q
superconducting microwave resonator, enabling such sensitive detection and
manipulation of electron degrees of freedom. Here we present the first
realization of a hybrid circuit in which a large number of electrons are
trapped on the surface of superfluid helium inside a coplanar waveguide
resonator. The high finesse of the resonator allows us to observe large
dispersive shifts that are many times the linewidth and make fast and sensitive
measurements on the collective vibrational modes of the electron ensemble, as
well as the superfluid helium film underneath. Furthermore, a large ensemble
coupling is observed in the dispersive regime during experiment, and it shows
excellent agreement with our numeric model. The coupling strength of the
ensemble to the cavity is found to be >1 MHz per electron, indicating the
feasibility of achieving single electron strong coupling.
