  We investigate the time evolution of the photon-detection probability at
various output ports of an all-fiber coupled cavity-quantum-electrodynamics
(cavity-QED) system. The setup consists of two atoms trapped separately in the
field of two nanofiber cavities that are connected by a standard optical fiber.
We find that the normal-mode picture captures well the main features of the
dynamics. However, a more accurate description based on the diagonalization of
a non-Hermitian Hamiltonian reveals the origin of small yet significant
features in the spontaneous emission spectra.
