  We present the experimental implementation of a two-qubit phase gate, using a
radio frequency (RF) controlled trapped-ion quantum processor. The RF-driven
gate is generated by a pulsed dynamical decoupling sequence applied to the
ions' carrier transitions only. It allows for a tunable phase shift with
high-fidelity results, in particular a fringe contrast up to $99_{-2}^{+1}\%$
is observed in Ramsey-type measurements. We also prepare a Bell state using
this laser-free gate. The phase gate is robust against common sources of error.
We investigate the effect of the excitation of the center-of-mass (COM) mode,
errors in the axial trap frequency, pulse area errors and errors in sequence
timing. The contrast of the phase gate is not significantly reduced up to a COM
mode excitation $<20$ phonons, trap frequency errors of +10%, and pulse area
errors of -8%. The phase shift is not significantly affected up to $<10$
phonons and pulse area errors of -2%. Both, contrast and phase shift are robust
to timing errors up to -30% and +15%. The gate implementation is resource
efficient, since only a single driving field is required per ion. Furthermore,
it holds the potential for fast gate speeds (gate times on the order of
$100~\mu$s) by using two axial motional modes of a two-ion crystal through
improved setups.
