Light enables manipulating many-body states of matter,and atoms trapped in optical lattices are a prominent example. However,quantum properties of light are completely neglected in all quantum gas experiments. Extending methods of quantum optics to many-body physics will enable phenomena unobtainable in classical optical setups. We show how using the quantum optical feedback creates strong correlations in bosonic and fermionic systems. It balances two competing processes,originating from different fields: quantum backaction of weak optical measurement and many-body dynamics,resulting in stabilized density waves and antiferromagnetic and NOON states. Our approach is extendable to other systems promising for quantum technologies.