| Summary: | Interactions between many-body atomic systems and light in cavities induce new atomic dynamics, which we show can be tailored by projective light measurement backaction, leading to collective effects such as density-density interactions, perfectly-correlated atomic tunneling, superexchange, and effective pair creation and annihilation. These can be long- and short-range, with tunable strengths, based on the optical setup. We show this provides a framework to enhance quantum simulations of novel physical phenomena, including reservoir models and dynamical gauge fields, beyond current methods.
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