  Light-matter interfaces enable the generation of entangled states of light
and matter which can be exploited to steer the quantum state of matter through
measurement of light and feedback. Here we consider continuous-time,
interferometric homodyne measurements of light on an array of light-matter
interfaces followed by local feedback acting on each material system
individually. While the systems are physically non-interacting, the feedback
master equation we derive describes driven-dissipative, interacting many-body
quantum dynamics, and comprises pairwise Hamiltonian interactions and
collective jump operators. We characterize the general class of
driven-dissipative many body systems which can be engineered in this way, and
derive necessary conditions on models supporting non-trivial quantum dynamics
beyond what can be generated by local operations and classical communication.
We provide specific examples of models which allow for the creation of
stationary many-particle entanglement, and the emulation of dissipative Ising
models. Since the interaction between the systems is mediated via feedback
only, there is no intrinsic limit on the range or geometry of the interaction,
making the scheme quite versatile.
