Coherent Inflation for Large Quantum Superpositions of Microspheres

We show that coherent inflation, namely quantum dynamics generated by inverted conservative potentials acting on the center of mass of a massive object, is an enabling tool to prepare large spatial quantum superpositions in a double-slit experiment. Combined with cryogenic, extreme high vacuum, and low-vibration environments, we argue that it is experimentally feasible to exploit coherent inflation to prepare the center of mass of a micrometer-sized object in a spatial quantum superposition comparable to its size. In such a hitherto unexplored parameter regime gravitationally-induced decoherence could be unambiguously falsified. We present a protocol to implement coherent inflation in a double-slit experiment by letting a levitated microsphere traverse a static potential landscape. Such a protocol could be experimentally implemented with an all-magnetic scheme using superconducting microspheres.