  In this report, the polarization properties of the photoluminescence emitted
by single nitrogen-vacancy (NV) color centers in diamond are investigated using
resonant excitation at cryogenic temperature. We first underline that the two
excited-state orbital branches are associated with two orthogonal transition
dipoles. Using selective excitation of one dipole, we then show that the
photoluminescence is partially unpolarized owing to fast relaxation between the
two orbitals induced by the thermal bath. This result might be important in the
context of the realization of indistinguishable single photons using NV defect
in diamond.
