  The image-charge detection provides a new direct method for the detection of
the Rydberg transition in electrons trapped on the surface of liquid helium.
The interest in this method is motivated by the possibility to accomplish the
spin state readout for a single trapped electron, thus opening a new pathway
towards using electron spins on liquid helium for quantum computing. Here, we
report on the image-charge detection of the Rydberg transition in a
many-electron system confined in an array of 20-um wide and 4-um deep channels
filled with superfluid helium. Such detection is made possible because of a
significant enhancement of the image-charge signal due to close proximity of
trapped electrons to the electrodes embedded in the microchannel structure. The
transition frequency of electrons in the range of 400-500~GHz is highly
controllable by the dc bias voltages applied to the device and is in a good
agreement with our calculations. This work demonstrates that microchannel
structures provide a suitable platform for electron manipulation and their
quantum state detection, with a feasibility of scaling the detection method to
a single electron.
