  We study two-level systems (2LS) coupled at different points to a
one-dimensional waveguide in which one end is open and the other is either open
(infinite waveguide) or closed by a mirror (semi-infinite). Upon injection of
two photons (corresponding to weak coherent driving), the resonance
fluorescence and photon correlations are shaped by the effective qubit
transition frequencies and decay rates, which are substantially modified by
interference effects. In contrast to the well-known result in an infinite
waveguide, photons reflected by a single 2LS coupled to a semi-infinite
waveguide are initially bunched, a result that can be simply explained by
stimulated emission. As the number of 2LS increases (up to 10 are considered
here), rapid oscillations build up in the correlations that persist for a very
long time. For instance, when the incoming photons are slightly detuned, the
transmitted photons in the infinite waveguide are highly antibunched. On the
other hand, upon resonant driving, incoherently reflected photons are mostly
distributed within the photonic band gap and several sharp side peaks. These
features can be explained by considering the poles of the single particle Green
function in the Markovian regime combined with the time delay. Our calculation
is not restricted to the Markovian regime, and we obtain several fully
non-Markovian results. We show that a single 2LS in a semi-infinite waveguide
can not be decoupled by placing it at the node of the photonic field, in
contrast to recent results in the Markovian regime. Our results illustrate the
complexities that ensue when several qubits are strongly coupled to a bus (the
waveguide) as might happen in quantum information processing.
