Probing into the gravity of quantum systems by levitated mechanics

We will report on our recent progress with experiments with trapped nano- and micro-particles, especially with Meissner-levitated ferromagnets above a type-1 superconductor. We find a system with ultralow mechanical damping showing great potential for sensing tiny forces and, apparently, independent from the standard quantum limit - which holds promise to detect record low magnetic fields and we discuss ideas for a ferromagnetic gyroscope, where the precession motional degree of freedom is used to sense tiny magnetic fields. We will further discuss how other rotational degrees of freedom can be used for inertial and force detection. We apply force noise measurements to bound collapse models to test the quantum superposition principle in the macroscopic domain of large-mass systems. We illustrate ideas to used levitated mechanical systems to probe into gravity interactions leading toward the experimental exploration of the interplay between quantum mechanics and gravity. We also illustrate ideas to probe into the physics of quantum field theory effects in non-inertial reference frames based on spinning micro-particles.