  To build up a collective emission, the atoms in an ensemble must coordinate
their behavior by exchanging virtual photons. We study this non-Markovian
process in a subwavelength atom chain coupled to a one-dimensional (1D)
waveguide and find that retardation is not the only cause of non-Markovianity.
The other factor is the memory of the photonic environment, for which a single
excited atom needs a finite time, the Zeno regime, to transition from quadratic
decay to exponential decay. In the waveguide setup, this crossover has a time
scale longer than the retardation, thus impacting the development of collective
behavior. By comparing a full quantum treatment with an approach incorporating
only the retardation effect, we find that the field memory effect,
characterized by the population of atomic excitation, is much more pronounced
in collective emissions than that in the decay of a single atom. Our results
maybe useful for the dissipation engineering of quantum information processings
based on compact atom arrays.
