  We report the design, fabrication, and characterization of a cryogenic ion
trap system for the implementation of quantum logic driven by near-field
microwaves. The trap incorporates an on-chip microwave resonator with an
electrode geometry designed to null the microwave field component that couples
directly to the qubit, while giving a large field gradient for driving
entangling logic gates. We map the microwave field using a single $^{43}$Ca$^+$
ion, and measure the ion trapping lifetime and motional mode heating rates for
one and two ions.
