We demonstrate the tunable enhancement of the zero phonon line of a single nitrogen-vacancy color center in diamond at cryogenic temperature. An open cavity fabricated using focused ion beam milling provides mode volumes as small as 1.24 $mu$m$^3$. In-situ tuning of the cavity resonance is achieved with piezoelectric actuators. At optimal coupling of the full open cavity the signal from individual zero phonon line transitions is enhanced by about a factor of 10 and the overall emission rate of the NV$^-$ center is increased by 40% compared with that measured from the same center in the absence of cavity field confinement. This result is important for the realization of efficient spin-photon interfaces and scalable quantum computing using optically addressable solid state spin qubits.
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