  We demonstrate coherent tunable coupling between a superconducting phase
qubit and a lumped element resonator. The coupling strength is mediated by a
flux-biased RF SQUID operated in the non-hysteretic regime. By tuning the
applied flux bias to the RF SQUID we change the effective mutual inductance,
and thus the coupling energy, between the phase qubit and resonator . We verify
the modulation of coupling strength from 0 to $100 MHz$ by observing modulation
in the size of the splitting in the phase qubit's spectroscopy, as well as
coherently by observing modulation in the vacuum Rabi oscillation frequency
when on resonance. The measured spectroscopic splittings and vacuum Rabi
oscillations agree well with theoretical predictions.
