  At the quantum many-body level, atom-light interfaces generally remain
challenging to solve for or understand in a non-perturbative fashion. Here, we
consider a waveguide quantum electrodynamics model, where two-level atoms
interact with and via propagating photons in a one-dimensional waveguide, and
specifically investigate the interplay of atomic position disorder, multiple
scattering of light, quantum nonlinear interactions and dissipation. We develop
qualitative arguments and present numerical evidence that such a system
exhibits a many-body localized~(MBL) phase, provided that atoms are less than
half excited. Interestingly, while MBL is usually formulated with respect to
closed systems, this system is intrinsically open. However, as dissipation
originates from transport of energy to the system boundaries and the subsequent
radiative loss, the lack of transport in the MBL phase makes the waveguide QED
system look essentially closed and makes applicable the notions of MBL.
Conversely, we show that if the system is initially in a delocalized phase due
to a large excitation density, rapid initial dissipation can leave the system
unable to efficiently transport energy at later times, resulting in a dynamical
transition to an MBL phase. These phenomena can be feasibly realized in
state-of-the-art experimental setups.
