  We investigate the radiative coupling between two two-level atoms with
arbitrarily polarized dipoles in the vicinity of a nanofiber. We present a
systematic derivation for the master equation, the single- and cross-atom decay
coefficients, and the dipole-dipole interaction coefficients for the atoms
interacting with the vacuum of the field in the guided and radiation modes of
the nanofiber. We study numerically the case where the atomic dipoles are
circularly polarized. In this case, the rate of emission depends on the
propagation direction, that is, the radiative interaction between the atoms is
chiral. We examine the time evolution of the atoms for different initial
states. We calculate the fluxes and mean numbers of photons spontaneously
emitted into guided modes in the positive and negative directions of the fiber
axis. We show that the chiral radiative coupling modifies the collective
emission of the atoms. We observe that the modifications strongly depend on the
initial state of the atomic system, the radiative transfer direction, the
distance between the atoms, and the distance from the atoms to the fiber
surface.
