  Controlling the spread of correlations in quantum many-body systems is a key
challenge at the heart of quantum science and technology. Correlations are
usually destroyed by dissipation arising from coupling between a system and its
environment. Here, we show that dissipation can instead be used to engineer a
wide variety of spatio-temporal correlation profiles in an easily tunable
manner. We describe how dissipation with any translationally-invariant spatial
profile can be realized in cold atoms trapped in an optical cavity. A uniform
external field and the choice of spatial profile can be used to design when and
how dissipation creates or destroys correlations. We demonstrate this control
by preferentially generating entanglement at a desired wavevector. We thus
establish non-local dissipation as a new route towards engineering the
far-from-equilibrium dynamics of quantum information, with potential
applications in quantum metrology, state preparation, and transport.
