  We develop a theory of electron transport in a double quantum dot device
recently proposed for the observation of the two-channel Kondo effect. Our
theory provides a strategy for tuning the device to the non-Fermi-liquid fixed
point, which is a quantum critical point in the space of device parameters. We
explore the corresponding quantum phase transition, and make explicit
predictions for behavior of the differential conductance in the vicinity of the
quantum critical point.
