  We analyze a nitrogen-vacancy (NV^-) colour centre based single photon source
based on cavity Purcell enhancement of the zero phonon line and suppression of
other transitions. Optimal performance conditions of the cavity-centre system
are analyzed using Master equation and quantum trajectory methods. By coupling
the centre strongly to a high-finesse optical cavity [Q ~ O(10^4-10^5), V ~
lambda^3] and using sub-picosecond optical excitation the system has striking
performance, including effective lifetime of 70 ps, linewidth of 0.01 nm, near
unit single photon emission probability and small [O(10^-5)] multi-photon
probability.
