Gravito-diamagnetic forces for mass independent large spatial superpositions

Abstract: Creating a massive spatial quantum superposition, such as the Schr\"odinger cat state, where the mass and the superposition size within the range $10^{-19}-10^{-14}$ kg and $\Delta x \sim 10~{\rm nm}-100~\mu {\rm m}$, is a challenging task. The methods employed so far rely either on wavepacket expansion or on a quantum ancilla, e.g. single spin dependent forces, which scale inversely with mass. In this paper, we present a novel approach that combines gravitational acceleration and diamagnetic repulsion to generate a large spatial superposition in a relatively short time. After first creating a modest initial spatial superposition of $1~\mu {\rm m}$, achieved through techniques such as the Stern-Gerlach (SG) apparatus, we will show that we can achieve an $\sim 10^{2}-10^{3}$ fold improvement to the spatial superposition size ($1~{\rm \mu m}\rightarrow 980~\mu {\rm m}$) between the wave packets in less than $0.02$~s by using the Earth's gravitational acceleration and then the diamagnetic repulsive scattering of the nanocrystal, neither of which depend on the object mass. Finally, the wave packet trajectories can be closed so that spatial interference fringes can be observed. Our findings highlight the potential of combining gravitational acceleration and diamagnetic repulsion to create and manipulate large spatial superpositions, offering new insights into creating macroscopic quantum superpositions.