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Interaction between macroscopic quantum systems and gravity

We review experiments and theoretical models about the possible mutual interplay between the gravitational field and materials in the superconducting state or other macroscopic quantum states. More generally, we focus on the possibility for quantum macrosystems in a coherent state to produce local alterations of the gravitational field in which they are immersed. This fully interdisciplinary research field has witnessed a conspicuous progress in the last decades, with hundreds of published papers, and yet several questions are still completely open.