Igor Mekhov

While optical lattices are well-established systems, the quantum nature of light is neglected in all setups so far. We show theoretically that the light quantization significantly broadens the range of physical phenomena. We prove that the quantum backaction of weak global measurement constitutes a novel source of competitions in many-body systems. This leads to novel effects beyond physics of open dissipative systems: multimode oscillations of macroscopic superposition states, protection and break-up of fermion pairs, as well as generation of antiferromagnetic states. Novel processes beyond standard Hubbard models can be designed by the measurement, entering the field of non-Hermitian many-body physics: long-range correlated pair tunnelling and Raman-like second-order transitions beyond typical quantum Zeno dynamics. We demonstrate the generation of multipartite mode entanglement and feedback control of many-body states out of reach of dissipative phase transitions.Quantization of optical lattice potentials enables quantum simulations of various long-range interacting systems unobtainable using classical optical lattices. This leads to new quantum phases (dimers, trimers, etc. of matter waves similar to valence bond solids) different from density orders (e.g. supersolids and density waves) directly benefiting from the collective light-matter interaction.