In the present work, we investigate the feasibility of a CNOT
gate that only uses the magnetic dipolar interaction between the
electron spin-1 carried by the NV 1 color center and the electron
spin-21 carried by the P1 center, a nearby nitrogen atom in
substitutional position [18]. This is a novel conception of the CNOT
gate that utilizes the impurity spins of diamond. As in the above-
mentioned ESR/NMR experiments, we consider the serial pulse
mode, more exactly two π=2-pulses separated by an interval of
time. Due to the decoherence, the duration of this free precession
between the two pulses should be limited. Here, it is calculated
rigourously. The first step is to establish the analytical expression
for the spin system response to a two-pulse sequence. It requires a
lot of algebra since the spin Hamiltonian includes the anisotropic
interaction between the triplet and the doublet, the hyperfine
interaction between the electron spin-21 and the nuclear spin-1 of
the P1 center and the Zeeman term.